If 0<x<1, then 1+x2xcoscot-1x+sincot-1x2-112=
x1+x2
x
1+x2
Explanation for correct option:
Step-1: Assume cot-1x=θ and finding sinθ,cosθ
Let, cot-1x=θx=cotθ
⇒sinθ=11+x2........i
⇒cosθ=x1+x2........ii
Step-2: Simplify the given data.
Given, 1+x2xcoscot-1x+sincot-1x2-112
=1+x2xcoscot-1x+sincot-1x2-112=1+x2x×x1+x2+11+x22-112fromequationi&ii=1+x2x2+11+x22-112=1+x21+x22-112=1+x21+x2-112=x1+x2
Hence, correct answer is option c