Question

Simplify the function: tan⁻¹ $\sqrt{\frac{1 - cos x}{1 + cos x}}$.

Answer 1

Answer:

The answer to this question is  " x/2 "

Step-by-step explanation:

I have used the Half Angle Identities to solve this question.

$1-cosx=2sin^{2}(x/2)$

$1+cosx=2cos^{2}(x/2)$

The given function is

$tan^{-1}\sqrt{\frac{1-cosx}{1+cosx}}\\\\=tan^{-1}\sqrt{\frac{2sin^{2}(x/2)}{2cos^{2}(x/2)}}\\\\=tan^{-1}\sqrt{tan^{2}(x/2)}}\\\\=tan^{-1}[tan(x/2)]\\\\=\frac{x}{2}$

Which is the most simplified from.

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