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:

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=π2But we cannot find C2 from given information          This question must be BONUS