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Next, we can express sinx and cosx in terms of tanx and secx. We will divide the numerator and denominator by cos2x: ∫sec2xsec2x+tanxdx. Step 3: Use substitutionLet t=tanx. Then, we have sec2xdx=dt. Substituting these into the integral gives: ∫1t2+t+1dt. Step 4: Completing...
Factorization is the decomposition of the terms of a mathematical expression into a multiplication of factors. In expressions with trigonometric functions, we can use identities to decompose the terms and perform the factorization through one of the existing methods. ...
then the value ofsin2xandcos2xcan also be obtained using the same formulas. In this case, we have the following special result: sin(2x)=2sinxcosxandcos(2x)=cos2x−sin2x. Answer and Explanation: Given Data: ...
derivative in any form, e.g.-sin x sin 2x+2cos x cos 2x Use double angle formula to express derivative in terms of sin x and cos x Equate derivative to zero and obtain an equation in one trig function Obtain 3 sin 2x=1, or 3 cos 2x=2 or 2 tan 2x=1Solve and obtainx=0.615 ...
Double angle identity for tan can be found by the formula; tan(A+B)=tanA+tanB1−tanAtanB We plug A=B and get; tan(2A)=2tanA1−tan2A Answer and Explanation:1 We have given; secx=14andsinx<0 ...
$\int\frac{1}{b^2}\frac{\frac{a^2}{b^2}\tan^2x+1}{\frac{a^4}{b^4}\tan^2x+1}dx$ I do not know how to solve it further. integration Share Cite Follow asked Feb 16, 2016 at 12:44 BrahmaguptaBrahmagupta 4,43422 gold badges4040 silver badges9696 bronze badges $\...
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?∫0π/2lncosxtanx⋅ln(lnsinxlncosx)dx=π24!? 5 How may be prove that ∫+∞−∞sin(coshx)cos(sinhx)dx=π2?∫−∞+∞sin(coshx)cos(sinhx)dx=π2? 3 Help to show if this is correct ∫∞0(e−2x...
NCERT solutions for CBSE and other state boards is a key requirement for students. Doubtnut helps with homework, doubts and solutions to all the questions. It has helped students get under AIR 100 in NEET & IIT JEE. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year pap...