Differentiate the following w.r.t x: cot^-1 √(1 + cosx / 1 - cos x)

Question

Differentiate the following w.r.t x: cot^-1\(\left(\sqrt{\cfrac{1+cos\,\text x}{1-cos\,\text x}}\right)\)

cot^-1√(1 + cos x / 1 - cos x)

Answer 1

To find: Value of cot^-1\(\left(\sqrt{\cfrac{1+cos\,\text x}{1-cos\,\text x}}\right)\)

Formula used: (i) sin 2θ = 2sin θ cos θ

(ii) 1 + cos θ = 2 cos²\(\cfrac{\theta}2\)

We have,  cot^-1\(\left(\sqrt{\cfrac{1+cos\,\text x}{1-cos\,\text x}}\right)\)