Question

$\tan \left(x-\frac{\pi}{2}\right) \cdot \cos \left(\frac{3 \pi}{2}+x\right)-\sin ^3\left(\frac{7 \pi}{2}-x\right)$ $\cos \left(x-\frac{\pi}{2}\right) \cdot \tan \left(\frac{3 \pi}{2}+x\right)$ when simplified reduces to:

• A. $\sin x \cos x$
• B. $-\sin ^2 x$
• C. $-\sin x \cos x$
• D. $\sin ^2 x$

Answer 1

Answer: (D)

$\frac{(-\cot x) \sin x+\cos ^3 x}{\sin x(-\cot x)}=\frac{-\cos x}{-\cos x}\left(1-\cos ^2 x\right)=\sin ^2 x$