The value of tan x sin
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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