Put x = a cosθ

⇒ tan^–1

⇒ tan^–1

⇒ tan^–1

Rationalising it

tan^–1

⇒ tan^–1

⇒ tan^–1

⇒ tan^–1

Cos θ = 1 – 2 sin² and sinθ =

⇒ 1 – cosθ = 2 sin²

= tan^–1

= tan^–1

= tan^–1(tan)

=

But θ = cos^–1

∴ The given equation simplification to cos^–1 .