Question

The value of \cos \left( \frac{3\pi }{2}+x \right)\,\cos \,(2\pi +x)\left\\{ \cot \left( \frac{3\pi }{2}-x \right)+\cot \,(2\pi +x) \right\\} is

• A. $0$
• B. $1$
• C. $cos\text{ }x$
• D. $sin\text{ }x$

Answer 1

Answer: (B)

$1$

Answer 2

$\cos \left( \frac{3\pi }{2}+x \right)\cos (2\pi +x)\,$
\left\\{ \cot \left( \frac{3\pi }{2}-x \right)\,+\cot \,(2\pi +x) \right\\} =\sin x.\cos x\,(\tan \,x+\,\cot \,x\\}
$=\sin x.\cos x\left( \frac{{{\sin }^{2}}x+{{\cos }^{2}}x}{\sin x.\cos x} \right)$
$=1$
$(\because \,\,\,{{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1)$