JEE MAIN - Mathematics Hindi (2024 - 29th January Morning Shift - No. 13)
$$x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$ के लिए यदि $$y(x)=\int \frac{\operatorname{cosec} x+\sin x}{\operatorname{cosec} x \sec x+\tan x \sin ^2 x} d x$$ है तथा $$\lim _\limits{x \rightarrow\left(\frac{\pi}{2}\right)^{-}} y(x)=0$$ है, तो $$y\left(\frac{\pi}{4}\right)$$ बराबर है
$$-\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)$$
$$\tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)$$
$$\frac{1}{2} \tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)$$
$$\frac{1}{\sqrt{2}} \tan ^{-1}\left(-\frac{1}{2}\right)$$
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