Question:
The value of $\tan x \sin \left(\frac{\pi}{2}+x\right) \cos \left(\frac{\pi}{2}-x\right)$
(a) 1
(b) $-1$
(c) $\frac{1}{2} \sin 2 x$
(d) none of these.
Solution:
(d) none of these.
We have:
$\tan \theta \sin \left(\frac{\pi}{2}+x\right) \cos \left(\frac{\pi}{2}-x\right)$
$=\frac{\sin x}{\cos x} \cos x \sin x$
$=\sin ^{2} x$
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