Mathematics · 2021
JEE Main · 27 August 2021, Shift 2 · Q67
If y(x)= cot^-1((√(1+ sin x)+√(1- sin x))/(√(1+ sin x)-√(1- sin x))), x ∈((π)/2, π), then (d y)/(d x) at x=(5 π)/6 is:
If $\displaystyle y(x)=\cot ^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right), x \in\left(\frac{\pi}{2}, \pi\right)$, then $\displaystyle \frac{\mathrm{d} y}{\mathrm{~d} x}$ at $\displaystyle x=\frac{5 \pi}{6}$ is :
Official answer
(2)
$\displaystyle -\frac{1}{2}$
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.