x3lim x2 2x 3x2 9. Prove that sin A - cos A 1&92;sin A cos A -1 1&92;sec A - tan A, using the identity sec 2 A1tan 2 A. Concept Notes &. a2 c2 b2 c2 c2 c2. Q 1. Ex 2. 5 Integrating powers of tangent and secant. m m is even or n n is odd Use either 1 1 or 2 2 (both will work). If v sec x then dv sec x tan x dx and tan x sec 2 x dx sec x(tan x sec x dx) v dv 1 v 2 C 2 1 sec 2 x C. Then you have a quadratic in sec . Rewrite tan(x) tan (x) in terms of sines and cosines. Here, notice that sec2x is already in the integral, and all that remains is tan2x. Rewrite sec(x) sec (x) in terms of sines and cosines. Since " sec2x 1 " is a difference of squares, it can be broken down into secx 1 and secx 1. View Solution. Question Papers 359. Click herepointup2to get an answer to your question writinghandprove that sec 6 theta tan. asked Dec 14, 2021 in Trigonometry by SatyamSarangi (36. This problem illustrates that there are multiple ways we can verify an identity. Trigonometry Simplify (tan (x)2) (sec (x)2) tan2 (x) sec2 (x) tan 2 (x) sec 2 (x) Rewrite tan2(x) sec2 (x) tan 2 (x) sec 2 (x) as (tan(x) sec(x))2 (tan (x) sec (x)) 2. P r o v e t h a t (1 tan A tan B) 2 (tan A tan B) 2 sec 2 A sec 2 B. Recall that we determined which trigonometric functions are odd and which are even. 3 Problem 15. (1 tanx) 1 tan2x 2tanx sec2x 2tanx. We know that cos2x. (sin x)(tan x cos x - cot x cos x) 1 - 2 cos2x 3. 052 2 k, 2 k. 1 sec cos. Learn how to prove the Pythagorean identity of secant and tan functions in mathematical form by geometrical method. Then you have a quadratic in sec . If tan2 1 - k2, show that sec tan3 cosec (2 - k2)32. sec c. Example 7. tan2x 1 - sec2x . Example Prove the identity sin 4 x - cos 4 x sin 2 x - cos 2 x. 1 Answer 1 vote. Find sec tan. You will notice that " secx 1 " appears both in the numerator and denominator, so they can both be cancelled out. sec 2 - tan 2 1 (which gives the relation between sec and tan) csc 2 - cot 2 1 (which gives the relation between csc and cot) Pythagorean Trig Identities. 1 tan x tan 2 x sec 2 x. View Solution. sec A-tan A 2 1-sin A 1 sin A. tan A sec A - 1 tan A sec A1 2 cosec A. 2 and pull out a sec 2 x in the integrand. Thus, 1 - tan 2 x 1 - (sec 2 x - 1) 2 - sec 2 x. View Solution. Sine, cosine, secant, and cosecant have period 2 while tangent and cotangent have period . Prove that. Solution Given sec 1312. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Q 5. Aug 5, 2015 at 1958. Explanation Left Hand Side sec2(x)-tan2x 1cos2x -(sin2x)cos2x (1-sin2x)cos2x cos2x. tan 2 1 sec 2 . The even-odd identities relate the value of a trigonometric function at a given angle to the value of the function at the opposite angle. We need to prove sec6 theta tan6 theta 3 tan2 theta sec2 theta 1 Solving the L. Write cos(x) cos (x) as a fraction with denominator 1 1. , LS RS. Click herepointup2to get an answer to your question writinghandfrac seca tana seca tana 1 2 seca. Prove the identity sec tan sec tan 1 2 sec tan 2 tan 2 . I have tried for an hour of substitution and everything but I haven't found the solution yet. In the second method, we split the fraction, putting both terms in the numerator over the common denominator. The minimum value of sin2cos2sec2cosec2tan2cot2. so if you could explain, I would greatly appreciate it. CISCE (English Medium) ICSE Class 10. Show that tan 4 tan 2 sec 4 - sec 2 . coesc 52. Click herepointup2to get an answer to your question writinghandsolve 1 cot a cosec a 1 tan a. In the first method, we used the identity sec 2 tan 2 1 sec 2 tan 2 1 and continued to simplify. State true (1) or false (0) The angle of elevation of the top of a tower is 300. Ex 2. Employing some creativity can sometimes simplify. Q 5. Prove that (sin cosec) 2 (cos sec) 2 7 tan 2 cot 2 . tan(x y) (tan x tan y) (1 tan x tan y). 052 2 k, 2 k. Question Papers 359. Answer link. View Solution. Given, (1 tan A tan B)2 (tan A - tan B)2 1 2 tan A tan B tan 2 A tan 2 B tan 2 A - 2tan A tan B tan 2 B 1 tan 2 A tan 2 A tan 2 B tan 2. 2 2 Differentiate x x and integrate sec2 x sec 2 x. Prove 1 cot2 csc2. tan sin cos. MCQ Online Mock Tests 19. tan sin cos. tan 2 1 sec 2 . Prove the following trigonometric identities. If the sum of coefficients in the expansion of (1xsinx2)n is P, then. I did that but I didn&39;t notice it was a quadratic, thank you TheNewGuy. The even-odd identities relate the value of a trigonometric function at a given angle to the value of the function at the opposite angle. Prove that 1. provecsc(2x)fracsec(x)2sin(x) provefracsin(3x)sin(7x)cos(3x)-cos(7x)cot(2x). Explanation Use tan2 sec2 1 to get. Prove that 1. further on solving you would get both sides equal to sec2 theta so. Mathematics General Solution of Trigonometric Equation Question Prove that (1tanA)2 (1tanA)2 2 sec2A Solution Verified by Toppr Take left hand side of the equation. If in aright angled greatest side is a, then tan equals. Question 29 Prove the following that- tan3(1 2) cot3(1 2) sec cosec 2 sin cos Solving LHS tan3(1 2) cot3(1 2) tan3(1 2) ()(. Now use this result in question, 2 (x 2 sec 2 x tan x) d x. cos 1sec 1213. Important Solutions 3394. At rst glance you may 2think you made a. Sure, there might be values of x for which the original equation works. tan2 sec 1 1 sec2 1 sec 1 1 (sec 1) 1 sec. Use app Login. Then the absolute value of 1(1f(r)) is. 6k points) inverse circular functions. Sign of Trigonometric Ratios in Different Quadrants. Therefore, x 3 2, 2 Now let sec1 (2) y that is secy 2. Table 1. Simon S. Prove trig expression Transform the left side of the expression LS sec4 x - tan4 x (sec2 x - tan2 x)(sec2 x tan2 x). View Solution. Then you have a quadratic in sec . Linear equation. We also know that sin 2 x cos 2 x 1 because this is a Pythagorean identity. Question Papers 359. That is, we have tanx in squared form accompanied by its derivative, sec2x. 1 Answer Sorted by 1 We have sin2(x) cos2(x) 1 sin 2 (x) cos 2 (x) 1. Cancel the common factor. It uses functions such as sine, cosine, and tangent to describe the ratios of the sides of a right triangle based on its angles. Substituting this identity in the given equation, we obtain tan21 22tan. This integral is ripe for substitution. prove&92;&92;csc(2x)&92;frac&92;sec(x)2&92;sin(x) prove&92;&92;frac&92;sin(3x)&92;sin(7x)&92;cos(3x)-&92;cos(7x)&92;cot(2x) prove&92;&92;frac&92;csc(&92;theta)&92;cot(&92;theta)&92;tan(&92;theta)&92;sin(&92;theta)&92;cot(&92;theta)&92;csc(&92;theta). Because sin 2 x cos 2 x 1, we can simplify the. tan A sec A - 1 tan A sec A1 2 cosec A. sec2(tan12) cosec2(cot13) . The sine of the negative angle is y. So (v) d v 1 2 v 2 1 2 sec 2 x. Oct 1, 2016 See explanation. 01 xex2dx. Click herepointup2to get an answer to your question writinghandtan2theta. Trigonometric Ratios of a Right Triangle. Then, divide all the terms by cos2x to derive a new identity sin2x cos2x cos2x cos2x 1 cos2x. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Now use this result in question, 2 (x 2 sec 2 x tan x) d x. Apply the product rule to 1 cos(x) 1 cos (x). Prove 1tan2thetasec2theta. f ln(sec x tan x) f ln (sec x tan x) Its easy to see that f sec x f sec x. For the next trigonometric identities we start with Pythagoras&x27; Theorem The Pythagorean Theorem says that, in a right triangle, the square of a plus the square of b is equal to the square of c a 2 b 2 c 2. Employing some creativity can. Pythagorean identities are identities in trigonometry that are extensions of the Pythagorean theorem. In the second method, we split the fraction, putting both terms in the numerator over the common denominator. When you started messing with the equation by. The formula for tan2x are tan2x sec2x - 1 tan 2 x sec 2 x - 1; tan2x sin2x cos2x tan 2 x sin 2 xcos 2 x; tan2x 1cot2x tan 2 x 1cot 2 x; What is the Difference Between tan2x and tan2x Tan2x is a double angle trigonometric formula which gives the value of the tangent function for the compound angle 2x. Feb 25, 2018 Given, (1 tan A tan B)2 (tan A - tan B)2 1 2 tan A tan B tan 2 A tan 2 B tan 2 A - 2tan A tan B tan 2 B 1 tan 2 A tan 2 A tan 2 B tan 2. I did that but I didn&39;t notice it was a quadratic, thank you TheNewGuy. Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step. Similar Questions. sec 6 tan 6 3 tan 2 sec 2 1 View Solution. Reciprocal Identities. cos2x cos2x -> Use Property sin2x cos2x 1 and isolate cos2x. Wolfram alpha agrees. View Solution. Explanation Use tan2 sec2 1 to get. CISCE (English Medium) ICSE Class 10. Prove that (tan A tan B) 2 (1 tan A tan B) 2 sec 2 A sec 2 B. In the first method, we used the identity sec 2 tan 2 1 sec 2 tan 2 1 and continued to simplify. Here are the identities that I used tan2theta1sec2theta tan2thetasin2thetacos2theta sin2thetacos2theta1 cos(2theta)cos2theta-sin2theta. View Solution. H e n c e, p r o v e d. 1 tan2 sec2. to prove. tan3x3C When working with integrals of tangent and secant, it may not always be apparent what to do. Simplify has a particular meaning in mathematics to rewrite with as few symbols as possible. Verified by Toppr. so the sum 3. 9 (940) Retired Math prof with teaching and tutoring experience in trig. arrow right. tan sin cos 4 53 5 4 3 tan sin cos 4 5 3 5 4 3. Tap for more steps. Concept Notes & Videos 195. 1 Answer Bdub Mar 20, 2018 See Below. Verified by Toppr. SimonS thank you, I got the answer it was (rounding decimals to three places) 1. cos2 sin2 1. Performing this integration yields u 3 3 C, and since u tan x, this becomes tan 3 x 3 C. Q5 (1 t a n A t a n B) 2 (t a n A t a n B) 2 s e c 2 A s e c 2 B . 3 The Pythagorean identities Remember that Pythagoras theorem states that in any right angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. Starting from cos2 (x) sin2 (x) 1 Divide both sides by cos2 (x) to get cos2 (x)cos2 (x) sin2 (x)cos2 (x) 1cos2 (x) which simplifies to. 1(Sec a - 1) 1(Sec a 1) 2 Cosec a Cot a. tan sec csc cot arcsin arccos arctan arcsec arccsc arccot. 2cos2 1 cos2. I feel that tan2(x) tan 2 (x) and sec2(x) sec 2 (x) are different enough functions that they cannot have the same derivative. SimonS thank you, I got the answer it was (rounding decimals to three places) 1. Start by simplifying the tan2 theta angle tan2 sin2cos2 1 << this we can agree on the solutions tell us to divide both sides by cos2. This leaves the case &92;(n&92;) odd and &92;(m&92;) even. Sign of Trigonometric Ratios in Different Quadrants. Leaving me with tan2 x tan2 x 0 tag2. 1 22 sec2. Trigonometric Substitution u atan() u a tan () The substitution u atan() u a tan () where u u is some function of x, x, a a is a real number, and 2 < < 2 2 < < 2 is often helpful when the integrand contains an expression of the form a2u2. Part A (1 tan 2 (x)) (sec 2 (x)) Answer Part B ((sec (x) tan (x)) (sec (x) tan (x))) (tan (x)) Answer. Use app Login. Let's give the integral we want the name I I int tan2xsec3x dx int (sec5x-sec3x)dx Next we'll integrate sec5x by parts. The points labelled 1, Sec(), Csc() represent the length of the line segment from the origin to that point. cos2 sin2 1. Use the fact that cot 2 () 1 csc 2 () to complete the following equality 1 Question 9. View Solution. (2) (sec tan) (1 sin) cos. a 2 u 2. Apr 30, 2023 Conditional trigonometrical identities. Nghi N. Solve for x tan(x)2sec(x)-10. arrow right. May 15, 2015. Pythagorean identities are useful in simplifying trigonometric expressions, especially in writing expressions as a function of. sec 2 (tan 1 2) csc 2 (cot 1 3) 1 tan 2. Periodicity of trig functions. 1 cot2 csc2. Find tan tan. 1 sin2x cos2x. Subtract 2 2 from 1 - 1. LHS sin 4 x - cos 4 x (sin 2 x) 2 - (cos 2 x) 2. Rewrite in terms of sines and cosines. (1tanx) sinx sinxcosx tanx. The Trigonometric Identities are equations that are true for Right Angled Triangles. Simultaneous equation. Step 1. cot x sec4x cot x 2 tan x tan3x 2. Solve 1tan2 1tan2 sec2. Click herepointup2to get an answer to your question writinghandfractanaseca1tanaseca1frac1sinacosa. d dx sin(x) cos(x) cos2(x) sin2(x) cos2(x) 1 cos2(x) sec2(x) d dx sin(x) cos(x) cos2(x) sin2(x) cos2(x) 1 sin2(x) cos2(x) 1 (sin(x) cos(x))2 1 tan2(x) Therefore 1 tan2(x) sec2(x) So is my prove valid, and are there. The answer is sec2theta We need tanthetasinthetacostheta sin2thetacos2theta1 1costhetasectheta The expression is 1tan2theta1sin2thetacos2theta (cos. View Solution. MCQ Online Mock Tests 19. Aug 5, 2015 at 1958. (28) cos 2 1 cos 2 2. 2 c) Compare the two results. View Solution. P r o v e t h a t (1 tan A tan B) 2 (tan A tan B) 2 sec 2 A sec 2 B. Reorder the polynomial. By doing tan2(x) sec2(x) 1 tan 2 (x) sec 2 (x) 1 we get. tanx 3 tan 3. Answer link. Similar Questions. Important Solutions 5478. RHS. so sin2cos2 cos2cos2 1cos2 and 1cos2 is sec2 << still following then somehow it says therefore tan2-1 sec2 so it replaces the entire first argument with sec2, completely ignoring. In fact, we use algebraic techniques constantly to simplify trigonometric. Apr 28, 2018 Explanation Let tan1(2) tan 2. I did that but I didn&39;t notice it was a quadratic, thank you TheNewGuy. Since " sec2x 1 " is a difference of squares, it can be broken down into secx 1 and secx 1. CBSE English Medium Class 10. a 2 b 2 c 2. Leaving me with tan2 x tan2 x 0 tag2. Use the fact that cot 2 () 1 csc 2 () to complete the following equality 1 Question 9. Then you have a quadratic in sec . Substituting this identity in the given equation, we obtain tan21 22tan. Aug 29, 2018 The value of sec2(tan1 2) cosec2(cot1 3) is (a) 12 (b) 5 (c) 15 (d) 9. I feel that tan2(x) tan 2 (x) and sec2(x) sec 2 (x) are different enough functions that they cannot have the same derivative. Part A (1 tan 2 (x)) (sec 2 (x)) Answer Part B ((sec (x) tan (x)) (sec (x) tan (x))) (tan (x)) Answer. Starting from cos2 (x) sin2 (x) 1 Divide both sides by cos2 (x) to get cos2 (x)cos2 (x) sin2 (x)cos2 (x) 1cos2 (x) which simplifies to 1tan2 (x) sec2 (x). craigslist north carolina fayetteville, hells angels calgary president
Check Trigonometry Formulas to get formulas related to trigonometry. . 1 tan 2 sec 2
Therefore, it is proved. An example of a trigonometric identity is. Given cot2(x)tan2(x)sec2(x)csc2(x)-2 Substitute sec2(x) 1 tan2(x). May 15, 2015. In calculus, trigonometric substitution is a technique for evaluating integrals. The identities 1 tan 2 sec 2 &92;displaystyle 1&92;tan 2&92;theta &92;sec 2&92;theta . Now consider g sin1(i tan(x)) g s i n 1 (i tan (x)) We have that g sec(x) g sec (x). View Solution. Message instructor about this question. sec2 5. This can be simplified to (a c)2 (b c)2 1. CISCE (English Medium) ICSE Class 10. Substituting this identity in the given equation, we obtain tan21 22tan. The secant and tan functions are written as &92;sec&92;theta and &92;tan&92;theta respectively in. sec 1 cos. 1 sec cos. 1, 14 (Method 1) Find the value of tan1 3 sec1(2) is equal to (B) 3 (C) 3 (D) 23 Solving tan1 Let y tan1 3 tan y 3 tan y tan () y Since Range of tan1 is (()2,2) Hence, principal value is 3 Solving sec1 (2) Let y sec1 (2) y sec1 (2) y . tan sin cos and. The fact that you can take the argument&x27;s "minus" sign outside (for sine and tangent) or eliminate it entirely (for cosine) can be helpful when working with. The most general solutions of the equation sec 2 x 2 (1 tan 2 x) are given by. cot2(x)tan2(x)(1 tan2(x))csc2(x)-2 Substitute csc2(x) 1cot2(x). Solve 1tan2 1tan2 sec2. We also know that sin 2 x cos 2 x 1 because this is a Pythagorean identity. Then, divide all the terms by cos2x to derive a new identity sin2x cos2x cos2x cos2x 1 cos2x. Starting from cos2 (x) sin2 (x) 1 Divide both sides by cos2 (x) to get cos2 (x)cos2 (x) sin2 (x)cos2 (x) 1cos2 (x) which simplifies to. Identities for. tan sin cos 4 53 5 4 3 tan sin cos 4 5 3 5 4 3. Since the first factor, (sec2 x - tan2 x) (1(cos2 x) - (sin2 x)(cos2 x)) (1 - sin2 x)(cos2 x) (cos2 x)(cos2 x) 1 There for, the left side becomes; LS (sec2 x tan2 x), and it equals the. Let tan 2 (x) sec 2 (x) 1 which comes from the Pythagorean identity I (sec 2 (x) 1) sec (x) d x sec 3 (x) d x sec (x) d x. Step 6. Prove that sin A - cos A 1sin A cos A -1 1sec A - tan A, using the identity sec 2 A1tan 2 A. Answer link. If the sum of coefficients in the expansion of (1xsinx2)n is P, then. answered Aug 29, 2018 by AbhishekAnand (88. Show that (1 sec 2) (1 sec 4) (1 sec 8) tan 8 tan . A follow up proof to accompany sin2 cos2 1. (sec A tan A 1) (sec A tan A. Answer link > sec (tan (-1) (2)) sqrt (5) Let theta tan (-1) (2) > tan theta 2 We know 1 tan2 theta sec2 theta > 1 22 sec2 theta > sec2 theta 5 > sec theta sqrt (5) > sec (tan (-1) (2)) sqrt (5). Alternatively, convert into sines and cosines and simplify. Maharashtra State Board SSC (Marathi Semi-English) 10th Standard Board Exam Question Papers 215. Find the other three trigonometric functions of from 1. Step 5. 1 22 sec2. In mathematics, trigonometric substitution is the replacement of trigonometric functions for other expressions. , LS RS. The identity 1 cot2 csc2 is found by rewriting the left side of the equation in terms of sine and cosine. 052 2 k, 2 k. Subtract 2 2 from 1 - 1. Cancel the common factor. Textbook Solutions 16764. (1cos2)sec2 tan. Simultaneous equation. coesc 52. csc (theta) 1 sin (theta) c a. Cuc s t&225;n ngi ho&224;n ho khi 'ha ngc' phi c Japan Airlines bc ch&225;y Tokyo 3 ph&250;t trc. They are distinct from triangle identities, which are. n &177; 4. 2sin(x 2) cos(x 2) cos2(x 2) 1. Rearranging, you absolutely get tan 2 x - sec 2 x 1. (x) (1tan2A 1cot2A) (1tanA 1cotA)2 tan2A. Prove the following. Detailed step by step solution for tan2(x)-sec(x)1. Iintsec3(x)dx-ln(abs(sec(x)tan(x))) The integral of sec3(x) can be found through integration by parts with usec(x) and. n &177; 4. Step 4. (sinx 1-cosx) (sinx1cosx) 2 csc x 5. The minimum value of sin2cos2sec2cosec2tan2cot2. View Solution. 231 2 k, 5. The points labelled 1, Sec(), Csc() represent the length of the line segment from the origin to that point. Like other methods of integration by substitution, when. Similar Questions. Step 2. I130 (3tan5 (2x)5tan3 (2x))C We want to solve Iinttan2 (2x)sec4 (2x)dx Rewrite the integrand using the trig identity color (blue) (sec2 (a)1tan2 (a) Thus Iinttan2 (2x) (1tan2 (2x))sec2 (2x)dx Make a substitution utan (2x)>du2sec2 (2x)dx I12intu2 (1u2)du color (white) (I)12intu4u2du color. 1 answer. cos 1sec 1213. Then substitute this for sec2(x) in the formula sec2(x) tan(x) 1. Pythagorean identities are identities in trigonometry that are extensions of the Pythagorean theorem. Prove that sin A - cos A 1sin A cos A -1 1sec A - tan A, using the identity sec 2 A1tan 2 A. Hence sin 25, cosec 52, cos 15, sec 5 and cot 12. Prove that following trigonometric identities cot2 1 sin21. Show that tan 4 tan 2 sec 4 - sec 2 . tan 2 (x) 1 sec 2 (x). Question Papers 991. sin2 cos2 1. Solution LHS tan 4 tan 2 . and sec2 x 1 cos2 45 (sqrt2)2 2. Solve the equation, sec22x 1tan2x. Answer link. Q 5. . View Solution. For the next trigonometric identities we start with Pythagoras&39; Theorem The Pythagorean Theorem says that, in a right triangle, the square of a plus the square of b is equal to the square of c a 2 b 2 c 2. Find the value of m for the given question sec 8 1 sec 4 1 m tan 8 tan 2 Q. Answer link. Solve 1tan2 1tan2 sec2. See the explanation section, below. If x a sec cos , y b sec sin and z c tan , then x2a2 y2b2 asked May 19, 2021 in Trigonometry by Gaatrika (32. This can be simplified to (a c)2 (b c)2 1. Using the identites 1 tan 2 A sec 2 A and 1 cot 2 A csc 2 A tan 2 A sec 2 A cot 2 A csc 2 A sin 2 A cos 2 A 1 cos 2 A cos 2 A sin 2 A 1 sin 2 A sin 2 A cos 2 A 1 R H S. 1tan2xsec2x Change to sines and cosines then simplify. 3 Problem 15. Show that tan 4 tan 2 sec 4 - sec 2 . &92;sec2x &92;,&92;, 1&92;tan2x &92;sec2A &92;,&92;, 1&92;tan2A Therefore, you can write the square of secant function formula in terms of any angle in this way in mathematics. and sec2 x 1 cos2 45 (sqrt2)2 2. tan(t) tan(t) Notice in particular that sine and tangent are odd functions , being symmetric about the origin, while cosine is an even function , being symmetric about the y -axis. tan(t) tan(t) Notice in particular that sine and tangent are odd functions , being symmetric about the origin, while cosine is an even function , being symmetric about the y -axis. The integrals secxdx sec. 11cosA tan 2 AsecA-1. Let f(x) be a real-valued function such that f(x)x f(x)x and f(x)0 for all real values of. Mar 9, 2018 Explanation LH S 2tan(x 2) 1 tan2(x 2) 2sin(x 2) cos(x 2) sec2(x 2) -> use the property 1 tan2x sec2x. If cot 3, find the value of cosec2 cot2 cosec2 sec2. Explanation From trigonometric identities, sin 2 x cos 2 x 1. Wolfram alpha agrees. (tan(x). 1 cos2xsin2x 2sin2xcos2x sin2xcos2x. This problem illustrates that there are multiple ways we can verify an identity. Open in App. sec 2 (tan 1 2) csc 2 (cot 1 3) 1 tan 2. See the proof below We need tanxsinxcosx sin2xcos2x1 secx1cosx Therefore, LHStan2x1 sin2xcos2x1 (sin2xcos2x)cos2x 1cos2x sec2x RHS QED. sec(x)tan2(x)dx sec3(x)dx sec(x)dx. . indeed greenville nc