Reduce to simplest form

tan^-1(xcosθ/1-xsinθ)
Take x=sin θ
=tan^-1(sinθcosθ/1-sin²Î¸)
=tan^-1(sinθcosθ/cos²Î¸)
=tan^-1(tanθ)
=θ=sin^-1x
tan^-1(xcosθ/1-xsinθ)=sin^-1x (1)

cot^-1(cosθ/x-sinθ)
Take x=cosecθ
=cot^-1(cosθ/(1/sinθ)-sinθ
=cot^-1(cosθsinθ/1-sin²Î¸)
=cot^-1(cosθsinθ/cos²Î¸)
=cot^-1(tanθ)
=cot^-1[cot((Π/2) -θ)]
=(Π/2)-θ =(Π/2)-cosec^-1x
cot^-1(cosθ/x-sinθ)=sec^-1x (2)
putting (1) and (2) in the given equation,we get
tan^-1(xcosθ/1-xsinθ) - cot^-1(cosθ/x-sinθ)=sin^-1x - sec^-1x
=sin^-1x- cos^-1(1/x)
wrong soln...

Thanks :)