∫d(cosθ)1-cos2θ=
cos-1θ+C
θ+C
sin-1θ+C
sin-1(cosθ)+C
Explanation for the correct option:
Evaluating the integral:
I=∫d(cosθ)1–cos2θ=–∫sinθdθ1–cos2θLett=cosθ⇒dt=-sinθdθI=∫dt1–t2substitutingtanddt=sin-1t+C=sin-1(cosθ)+C
Therefore, ∫d(cosθ)1-cos2θ=sin-1(cosθ)+C
Hence the correct answer is option (D).