MCQ
${d \over {dx}}\left[ {\log \sqrt {{{1 - \cos x} \over {1 + \cos x}}} } \right] = $
- A$\sec x$
- ✓$cosec\,x$
- C$cosec{x \over 2}$
- D$\sec {x \over 2}$
✓
Answer
Correct option: B.
$cosec\,x$
b
(b) $\frac{d}{{dx}}\left[ {\log \sqrt {\frac{{1 - \cos x}}{{1 + \cos x}}} } \right] = \frac{d}{{dx}}\left[ {\log \left( {\tan \frac{x}{2}} \right)} \right] = {\rm{cosec}}\,x$.
(b) $\frac{d}{{dx}}\left[ {\log \sqrt {\frac{{1 - \cos x}}{{1 + \cos x}}} } \right] = \frac{d}{{dx}}\left[ {\log \left( {\tan \frac{x}{2}} \right)} \right] = {\rm{cosec}}\,x$.
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