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) $\frac{1}{2}\sin 2x$
(d) none of these.

Answer 1

(d) none of these

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{tan\theta }\sin \left(\frac{\mathrm{\pi }}{2}+x\right)\cos \left(\frac{\mathrm{\pi }}{2}-x\right) \\ =\frac{\sin x}{\cos x}\cos x\sin x \\ ={\sin }^{2}x \end{gathered}$$