Let f(x)=sintan-1x+sincot-1x2-1,|x|>1. If dydx=12ddxsin-1(f(x)) and y(3)=π6 then y(-3) is equal to:
-π6
5π6
π3
2π3
Let tan-1x=θ θ∈-π2,-π4∪π4,π2 as |x|>1∴f(x)=(sinθ+cosθ)2-1=sin2θ=2x1+x2 Now sin-1f(x)=sin-1sin2θ=-π-2θ,θ∈-π2,π4π-2θ, θ∈π4,π2∴ddxsin-1f(x)=-11+x2,|x|>1 ∴dydx=-11+x2⇒y=C1-tan-1x,x>1C2-tan-1x, x<-1 y(3)=π6⇒C1=π2
But we cannot find C2 from given information
This question must be BONUS