`1/(cos^2 x) 1/(sin^2 x)` =>Use the identities sec^2 (x) = tan^2 (x) 1 and csc^2 (x) = 1 cot^2 (x), both are derived from the pythagorean identity of 1 = sin^2 (x) cos^2 (x) by dividing through by either sin 2 or cos 2 2 View Entire Discussion (1 Comments) More posts from the cheatatmathhomework community 51 Posted by u/Obig_ProffesorSeparate fractions Rewrite tan(x) tan ( x) in terms of sines and cosines Multiply by the reciprocal of the fraction to divide by sin(x) cos(x) sin ( x) cos ( x) Convert from cos(x) sin(x) cos ( x) sin ( x) to cot(x) cot ( x) Divide sec2(x) sec 2 ( x) by 1 1 Rewrite sec(x) sec (
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Tan^2x+sec^2x=1-Integrating Al and Bl wrt x, We have A — sin 2x— log ( sec 2x tan 2N )CI B — cos2x Hence complete solution is y— cos 2x c2 sin2x — cos 2x log (sec 2x tan 2x) Ans EM52 Q14 Solve d2y dy 3 v2 dv BTech (11 serm) Hence the given equation is not exact therefore to use an integration factor here to change the given' h intoAnswer requested by Bhupinder Singh
The Integral Int Sec 2x Secx Tanx 9 2 Dx Equals For Some Arbitrary Constant K Dot 1 Secx Tanx 11 2 1 11 1 7 Secx Tanx 2 K 1 Secx Tanx 1 11 1 11 1 7 Secx Tanx 2 K 1 Secx Tanx 11 2 1 11 1 7 Secx Tanx 2 K 1
The derivative of tan 2x is 2 sec 2 (2x) (ie) d/dx tan 2x = 2 sec 2 (2x) Explanation We know that the derivative of tan x is sec 2 x (ie) d/dx (tan x) = sec 2 x According to the chain rule,SOLUTION verify the idenity sec^4x – sec^2x = tan^4x tan^2x'' Log On Algebra Trigonometry Section Solvers Solvers Lessons Lessons Answers archive Answers Click here to see ALL problems on Trigonometrybasics;Author has 96K answers and 68M answer views sec^2 (2x) = 1 tan (2x) 1 tan^2 (2x) = 1 tan (2x) tan^2 (2x) tan (2x) = 0 tan (2x) tan (2x) 1
=0 (2k 1) !Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreHi Simplifying the following (sec^2x csc^2x)(tan^2x cot^2x) tan^2x = sec^2x 1 cot^2x = csc^2x 1
Ved Prakash Sharma , former Lecturer at Sbm Inter College, Rishikesh () Answered 3 years ago Trigonometric Simplification Calculator \square!Integration by Substitution Put sec 2 x = t 2 sec 2 x tan 2 x d x = d t Now sec 2 x tan 2 x d x = 2 d t
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Rewrite sec(x) sec ( x) in terms of sines and cosines Rewrite tan(x) tan ( x) in terms of sines and cosines Multiply by the reciprocal of the fraction to divide by 1 cos(x) 1 cos ( x) Write cos(x) cos ( x) as a fraction with denominator 1 1 Cancel the common factor of cos(x) cos ( x)Sec^4x Tan^4x = Sec^2x Tan^2x math use the quotient and reciprocal identities to simplify the given expression cot t sin t csc t sin t tan t cot t cot t sec t math Find the values of the trigonometric function cot 8/17 sin sec tan cot I know you use a Pythagorean Identity, sin^2t cos^2t=1 I got 64/2 for the first one forWe have to prove `(tan x cot x)^2 = sec^2 x cosec^2x` `sec^2x cosec^2x` =>
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Solving the value of $x$ for the equation $\frac {(\sec x \tan x)^2 (\sec 2x \tan x)^2}{\sin 2x \sin x} = 2$Y=sec x tan x By product rule, f= secx, g=sec^2x and f dash= secx tanx, g dash= sec^2x Next, y dash= sec x⋅sec^2 x tan x⋅sec x tan x Next, y dash= sec x (sec^2 x tan^2 x) Derivative of sec square x Let, sec x is equal to y Now the derivative of sec squared x equals the derivative y squareEx 73, 15 tan3 2 sec 2 Let I= 3 2 sec 2 = tan 2 2 tan 2 sec 2 = sec 2 2 1 2 sec 2 Putting sec 2 = Differentiating wrtx sec 2 = 2 sec 2 tan 2 = = 2 sec 2 tan 2 Putting values of sec 2x and dx in equation I = sec 2 2 1 2
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About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy &TRIGONOMETRY LAWS AND IDENTITIES DEFINITIONS sin(x)= Opposite Hypotenuse cos(x)= Adjacent Hypotenuse tan(x)= Opposite Adjacent csc(x)=This is readily derived directly from the definition of the basic trigonometric functions sin and cos and Pythagoras's Theorem Divide both side by cos^2x and we get sin^2x/cos^2x cos^2x/cos^2x = 1/cos^2x tan^2x 1 = sec^2x tan^2x = sec^2x 1 Confirming that the result is an identity Answer link
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The Second Derivative Of tan^2x To calculate the second derivative of a function, differentiate the first derivative From above, we found that the first derivative of tan^2x = 2tan(x)sec 2 (x) So to find the second derivative of tan^2x, we need to differentiate 2tan(x)sec 2 (x) We can use the product and chain rules, and then simplify to find the derivative ofThey use the key relations sin 2 x cos 2 x = 1 \sin^2x \cos^2x = 1 sin 2 x cos 2 x = 1, tan 2 x 1 = sec 2 x \tan^2x 1 = \sec^2x tan 2 x 1 = sec 2 x, and cot 2 x 1 = csc 2 x \cot^2x 1 = \csc^2x cot 2 x 1 = csc 2 x to manipulate an integral into a simpler form The derivatives of trigonometric functionsSafety How works Test new features Press Copyright Contact us Creators
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Sen ^2 (x) cos ^2 (x) = 1 tan ^2 (x) 1 = sec ^2 (x) cot ^2 (x) 1 = csc ^2 (x) sen(x y) = sen x cos y cos x sen y cos(x y) = cos x cosy sen x sen y1tan^2(x) = 1 (sin 2 x)/(cos 2 x) = cos 2 x sin 2 x/cos 2 x = cos 2x/cos 2 x is a posibly 'simplified' version in that it has been boiled down to only cosines 1 tan 2 = sec 2 x note the positive sign The given expression does not have a simplificationThe number of solution of the equation `tan^2xsec^(10)x1=0` in (0,10) is Updated On 187 To keep watching this video solution for FREE, Download our App Join the 2 Crores Student community now!
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=2sec^4(x)sec^2(x)2sec^2(x)sec(x)tan(x) The integrals of the second and third functions are standard!Watch Video in App Continue on Whatsapp This browser does not support the video elementIntegrate ∫ tan 3 2x sec 2x dx class12;
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Yes, sec 2 x−1=tan 2 x is an identity sec 2 −1=tan 2 x Let us derive the equation We know the identity sin 2 (x)cos 2 (x)=1 ——(i) Dividing throughout the equation by cos 2 (x) We get sin 2 (x)/cos 2 (x) cos 2 (x)/cos 2 (x) = 1/cos 2 (x) We know that sin 2 (x)/cos 2 (x)= tan 2 (x), and cos 2 (x)/cos 2 (x) = 1 So the equation (i) after substituting becomesSearch the world's information, including webpages, images, videos and more Google has many special features to help you find exactly what you're looking forIntegral of tan (2x)sec^2 (2x) \square!
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A =erf2 (ax) x erf (ax) exp (a~x~) 2 (4a2x2) h' 2 y;\sec(2x^{1}1)\tan(2x^{1}1)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}1) The derivative of a polynomial is the sum of the derivatives of its terms The derivative of a constant term is 0To integrate sec^4(x), there is a reduction formula, which I will post in a separate comment in a few minutes, but which must appear in calculus texts
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Share It On Facebook Twitter Email 1 Answer 1 vote answered by AmirMustafa (600k points) selected by Vikash Kumar Best answer Given 2x = sec A ← PrevSo sec^2 (x)=1tan^2 (x) This is one of the three Pythagorean identities in trigonometry, but if you don't recognize it, try converting to sines and cosines 1/cos^2 (x)=1sin^2 (x)/cos^2 (x) Now, multiply each term by cos^2 (x) to get 1=cos^2 (x) sin^2Share It On Facebook Twitter Email 1 Answer 1 vote answered by Swara (803k points) selected by Vikash Kumar Best answer The given integral I = ∫ tan 3 2x sec 2x dx = ∫ tan 2 2x
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Antiderivative of 2tan x sec x Compute tan x sec 2 x dx in two different ways a) By substituting u = tan x b) By substituting v = sec x c) Compare the two results Solution a) Compute tan x sec 2 x dx by substituting u = tan x If u = tan x 2then du = sec x dx and tan x sec 2 x dx = u du = 1 u2 c 2 = 1 tan2 x c 2Definitions Trigonometric functions specify the relationships between side lengths and interior angles of a right triangle For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse The six trigonometric functions are defined for every real number, except, for some of them\\int \tan^{2}x\sec{x} \, dx\ >
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Click here👆to get an answer to your question ️ inttan^3 2x sec 2x dx Join / Login >>1 = (sec(x))2 (tan(x))2 Now, we will see if 1 = (sec(x))2 (tan(x))2and 1 = (sec(x))2 (tan(x))2 can both be true We can do this by assuming that they are both true, and then add the equations to get 2 = 2(sec(x))2 1=(sec(x))2 But we know what values of x can make this true, don't we )Ex 34, 8 Find the general solution of the equation sec2 2x = 1 – tan 2x sec2 2x = 1 – tan 2x 1 tan2 2x = 1 – tan2x tan2 2x tan2x = 1 – 1 tan2 2x tan2x = 0 tan 2x (tan2x 1) = 0 Hence We know that sec2 x = 1 tan2 x So, sec2 2x = 1 tan2 2x tan 2x = 0 ta
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(We use the identity {eq}1tan^2(x)=sec^2(x) {/eq} {eq}\tan^2 x = \tan^2x {/eq} (The ones cancel and we are done) Become a member and unlock all Study Answers Try it riskfree for 30 days Try itProve tan^2(x) (1cot^2x) = sec^2x Prove tan^{2}(x) (1cot^{2}x) = sec^{2}x ar Related Symbolab blog posts Spinning The Unit Circle (Evaluating Trig Functions )An alternative method is to take `sec^2 x ` and replace it by `1/(cos^2 x)` Replace `1/(cos^2 x)` by `1 tan^2 x` (the basic formula of trigonometry `1tan^2 x = 1/(cos^2 x)` )
The Integral Int Sec 2x Secx Tanx 9 2 Dx Equals For Some Arbitrary Constant K Dot 1 Secx Tanx 11 2 1 11 1 7 Secx Tanx 2 K 1 Secx Tanx 1 11 1 11 1 7 Secx Tanx 2 K 1 Secx Tanx 11 2 1 11 1 7 Secx Tanx 2 K 1
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Use the identity $1\tan ^{2}(x)=$ $\sec ^{2}(x)$ to convert the given integral to one that involves only $\tan (x)$ or only $\sec (x)$ Then use reduction formula (6213) or formula (6214) to evaluate the given indefinite integral $$ \int_{0}^{\pi / 4} \sec ^{4}(x) \tan ^{2}(x) d x $$If 2x = sec A and 2/x = tan A prove that (x 2 1/x 2) = 1/4 trigonometric identities;This video shows how to find the integral of sec(2x)*tan(2x)
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The Second Derivative Of sec^2x To calculate the second derivative of a function, differentiate the first derivative From above, we found that the first derivative of sec^2x = 2sec 2 (x)tan(x) So to find the second derivative of sec^2x, we need to differentiate 2sec 2 (x)tan(x) We can use the product and chain rules, and then simplify to find the derivative of 2sec 2 (x)tan(x) isUsiong sec 2θ−tan 2θ=1⇒(2x) 2−( x2 ) 2=1, substitute the given values in terms of x⇒4x 2− x 24 =1⇒4(x 2− x 21 )=1⇒x 2− x 21 = 41Get stepbystep solutions from expert tutors as fast as 1530 minutes
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Sin ^2 (x) cos ^2 (x) = 1 tan ^2 (x) 1 = sec ^2 (x) cot ^2 (x) 1 = csc ^2 (x) sin(x y) = sin x cos y cos x sin y cos(x y) = cos x cosy sin x sin yIt is easy to integrate this, as the integral of sec^2 (2x) = 05tan (2x) and the integral of cosec^2 (2x) = 05cot (2x) Hence, the integral of tan (2x) cot (2x)^2 = 05tan (2x) 05cot (2x c 701 views Phương trình 2cot 2x 3cot 3x = tan 2x có
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đề môn Toán thi THPT QUốc Gia 21 Trang chủ Lớp 11 Toán 11 Toán lớp 11 I Lượng giácGet stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!(sec^2x csc^2x)(tan^2x cot^2x) Found 2 solutions by ewatrrr, MathLover1 Answer by ewatrrr(243) (Show Source) You can put this solution on YOUR website!
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Here we will prove the problems on trigonometric identities As you know that the identity consists of two sides in equation, named Left Hand Side (abbreviated as LHS) and Right Hand Side (abbreviated as RHS)To prove the identity, sometimes we need to apply more fundamental identities, eg $\sin^2 x \cos^2 x = 1$ and use logical steps in order to lead one
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