Prove the following : tan^-1 √(1-cos θ/1+ cosθ​​​​​​​) , if θ ∈ (0, π)

Question

Prove the following :

tan^-1\(\sqrt{\cfrac{1-cos\,θ}{1+cos\,θ}}\) = \(\cfrac{θ}{2}\), if θ ∈ (0, π)

tan^-1 √(1-cos θ/1+ cosθ) , if θ ∈ (0, π)

Answer 1

tan^-1\(\sqrt{\cfrac{1-cos\,θ}{1+cos\,θ}}\) = \(\cfrac{θ}{2}\)