MCQ
${d \over {dx}}\left[ {\left( {{{{{\tan }^2}2x - {{\tan }^2}x} \over {1 - {{\tan }^2}2x{{\tan }^2}x}}} \right)\cot 3x} \right] =$
- A$\tan 2x\,\tan x$
- B$\tan 3x\tan x$
- ✓${\sec ^2}x$
- D$\sec x\tan x$
$= \frac{{(\tan 2x - \tan x)}}{{(1 + \tan 2x\tan x)}}\,\frac{{(\tan 2x + \tan x)}}{{(1 - \tan 2x\tan x)}}$
$= \tan (2x - x)\,\tan (2x + x)$$ = \tan x\tan 3x$.
$\therefore$ $\frac{d}{{dx}}[y.\cot 3x] = \frac{d}{{dx}}[\tan x] = {\sec ^2}x$.
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