Question

Prove that ∫dx/(a – cos x) for x ∈ [0,π] = π/√(a² – 1).a > 1 and deduce that ∫dx/(2 – cos x)² = 2π/3√3 for x ∈ [0,π].

Answer 1

We have, 

Diffeerentiating w.r.t a, we get