Mathematics

Problem

Let

f(x) = (\sin(\tan^{-1}x) + \sin(\cot^{-1}x))^2 - 1

|x| > 1

. If

\frac{dy}{dx} = \frac{1}{2} \frac{d}{dx} (\sin^{-1}(f(x)))

and

y(\sqrt{3}) = \frac{\pi}{6}

, then

y(-\sqrt{3})

is equal to [JEE-MAIN ONLINE-2020] (1)

\frac{5\pi}{6}

(2)

-\frac{\pi}{6}

(3)

\frac{\pi}{3}

(4)

\frac{2\pi}{3}