Prove the following : tan^-1[(cos θ + sin θ)/(cos θ- sinθ)] = π/4 + θ if θ ∈(-π/4, π/4)

Question

Prove the following :

tan^-1 \(\left[\cfrac{cos\,θ+ sin\,θ}{cos\,θ - sin\,θ}\right]\) = \(\cfrac{\pi}{4}\)+ θ if θ ∈ \(\left(-\cfrac{\pi}{4},\cfrac{\pi}{4}\right)\)

tan^-1[(cos θ + sin θ)/(cos θ- sinθ)] = π/4 + θ if θ ∈(-π/4, π/4)

Answer 1

 tan^-1 \(\left[\cfrac{cos\,θ+ sin\,θ}{cos\,θ - sin\,θ}\right]\) = \(\cfrac{\pi}{4}\)+ θ if θ ∈ \(\left(-\cfrac{\pi}{4},\cfrac{\pi}{4}\right)\)