4 / 4 d x 1 + cos 2 x is equal to:

Question

$\int_{- π / 4}^{π / 4} \frac{d x}{1 + \cos 2 x}$ is equal to:

Smart Achievers · Accepted Answer

(1)

Ans. 1

Explanation :

Let $I = \int_{- π / 4}^{π / 4} \frac{d x}{1 + \cos 2 x}$

$= \int_{- π / 4}^{π / 4} \frac{d x}{2 \cos^{2} x}$

$= \frac{1}{2} \int_{- π / 4}^{π / 4} \sec^{2} x d x = \int_{0}^{π / 4} \sec^{2} x d x$

$= {[\tan x]}_{0}^{π / 4} = \tan \frac{π}{4} - \tan 0$

$= 1 - 0 = 1$

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