For x \in (-\frac{\pi}{2}, \frac{\pi}{2}), if y(x)=\int {{\cosec} x+ \sin x}/{{\cosec} x \sec x+\tan x \sin ^2 x} \dx and \lim_{x \to (\frac{\pi}{2}) ^{-}} y(x)=0 then y (\frac{\pi}{4}) is equal to [29-Jan-2024 Shift 1]

Correct Answer is : 1√2tan−1(−12)

\frac{1}{2} \tan ^{-1} ( {1}/{\sqrt{2}})

- {1}/{\sqrt{2}} \tan ^{-1} ( {1}/{\sqrt{2}})

{1}/{\sqrt{2}} \tan ^{-1} (-\frac{1}{2})

Indefinite Integrals

Section: Mathematics

Question : 21 of 89

Marks: +1, -0

For x∈(−‌

,‌

),
if y(x)=∫‌

cosec‌x+sin‌x

cosec‌x‌sec‌x+tan‌x‌sin‌2x

‌dx
and

lim

x→(‌

)−

y(x)=0 then y(‌

) is equal to

[29-Jan-2024 Shift 1]

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