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Inverse Trigonometric Functions — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSInverse Trigonometric Functions2 Marks
Question
Write the function in the simplest form: ${\tan ^{ - 1}}\sqrt {\frac{{1 - \cos x}}{{1 + \cos x}}} ,\;0<x < \pi $
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Answer

${\tan ^{ - 1}}\sqrt {\frac{{1 - \cos x}}{{1 + \cos x}}}$
$= {\tan ^{ - 1}}\sqrt {\frac{{2{{\sin }^2}\frac{x}{2}}}{{2{{\cos }^2}\frac{x}{2}}}}$
$ = {\tan ^{ - 1}}\tan \frac{x}{2}$
$= \frac{x}{2}$

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