Question

If $x\ne 0$, then $\frac{\sin (\pi+x) \cos \left(\frac{\pi}{2}+x\right) \tan \left(\frac{3 \pi}{2}-x\right) \cot (2 \pi-x)}{\sin (2 \pi-x) \cos (2 \pi+x) \text{cosec}(-x) \sin \left(\frac{3 \pi {2}+x\right)}=$

• A. 0
• B. -1
• C. 1
• D. 2

Answer 1

Answer: (C)

$\sin (\pi +x)\cos \left(\frac{\pi }{2}+x\right)\tan \left(\frac{3\pi }{2}-x\right)\cot (2\pi -x)$
$\sin (2\pi -x)\cos (2\pi +x)\text{cosec}(-x)\sin \left(\frac{3\pi }{2}+x\right)$
$=x\ne 0$
$\sin (\pi +x)\cos \left(\frac{\pi }{2}+x\right)\tan \left(\frac{3\pi }{2}-x\right)\cot (2\pi -x)$
$\sin (2\pi -x)\cos (2\pi +x)\text{cosec}(-x)\sin \left(\frac{3\pi }{2}+x\right)$