If y(x) Is Defined Using an Integral.....

JEE MAIN

29-01-24 S1

Question

For $\mathrm{x} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, if $y(x)=\int \frac{\operatorname{cosec} x+\sin x}{\operatorname{cosec} x \sec x+\tan x \sin ^2 x} d x$ and $\lim _{x \rightarrow\left(\frac{\pi}{2}\right)^{-}} y(x)=0$ then $y\left(\frac{\pi}{4}\right)$ is equal to

Select the correct option:

$\tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)$

$\frac{1}{2} \tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)$

$-\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)$

(4) $\frac{1}{\sqrt{2}} \tan ^{-1}\left(-\frac{1}{2}\right)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution