Let ƒ(x) = (sin(tan^–1x) + sin(cot^–1x))² – 1, |x| > 1. If dy/dx = 1/2d/dx(sin ⁻¹(f(x))) and y(3) = (π)/6, then y(- 3) is equal to:

Limit, Continuity and Differentiability: JEE Main 2020 Mathematics question

JEE Main 2020 · 8 Jan, Morning shift · Q3679

JEE Main 20208 Jan, Morning shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let ƒ(x) = (sin(tan^–1x) + sin(cot^–1x))² – 1, |x| > 1. If

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

and

y\left( {\sqrt 3 } \right) = {\pi \over 6}

, then y(

{ - \sqrt 3 }

) is equal to :

JEE Main 2020 · 8 Jan, Morning shift · Q3679

JEE Main 20208 Jan, Morning shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let ƒ(x) = (sin(tan^–1x) + sin(cot^–1x))² – 1, |x| > 1. If

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

and

y\left( {\sqrt 3 } \right) = {\pi \over 6}

, then y(

{ - \sqrt 3 }

) is equal to :