Prove the following : cos^-1 x = π + tan^-1 √(1-x^2)/x

Question

Prove the following :

cos^-1 x = π + tan^-1 \(\cfrac{\sqrt{1-x^2}}{x}\)

cos^-1 x = π + tan^-1 √(1-x²)/x

Answer 1

Let cos^-1 x = \(\alpha\).