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  • Need solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 26

Need solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 26

Answers (1)

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\tan x-x+c

Hint: To solve this equation we use \cos 2x, \int sec^{2} xdx formula

\begin{aligned} &\text { Given: } \int \frac{1-\cos 2 x}{1+\cos 2 x} d x\\ &\text { Solution: }\\ &\int \frac{1-\cos 2 x}{1+\cos 2 x} d x\\ &\int \frac{2 \sin ^{2} x}{2 \cos ^{2} x} d x \quad\left[\begin{array}{l} \cos 2 x=1-2 \sin ^{2} x \\ \cos 2 x=2 \cos ^{2} x-1 \end{array}\right]\\ &\int \tan ^{2} x d x\\ &\int \sec ^{2} x d x-\int 1 d x \quad\left[\begin{array}{l} \sec ^{2} x-\tan ^{2} x=1 \\ \sec ^{2} x-1=\tan ^{2} x \\ \int \sec ^{2} x d x=\tan x+c \end{array}\right]\\ &\tan x-x+c \end{aligned}

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