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Trigonometric Ratios of Compound Angles

Evaluate: t...

Question

Evaluate: ${t a n}^{- 1} (\sqrt{\frac{1 - c o s x}{1 + c o s x}})$

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Solution

$t a n^{- 1} \sqrt{\frac{1 - c o s x}{1 + c o s x}}$

$= t a n^{- 1} \sqrt{\frac{2 s i n^{2} \frac{x}{2}}{2 c o s^{2} \frac{x}{2}}}$

$= t a n^{- 1} t a n \frac{x}{2}$

$= \frac{x}{2}$

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