Q (8) Prove the following

\small \frac{\cos (\pi +x)\cos (-x)}{\sin (\pi -x)\cos \left ( \frac{\pi }{2}+x \right )} = \cot ^{2} x

 

Answers (1)
S safeer

As we know that,
\cos(\pi+x) = -\cos x   ,  \sin (\pi - x ) = \sin x    ,  \cos \left ( \frac{\pi}{2} + x\right ) = - \sin x              
and 
\cos (-x) = \cos x  

By using these our equation simplify to

\frac{\cos x \times -\cos x}{sin x \times - \sin x} = \frac{- \cos^{2}x}{-\sin^{2}x} = \cot ^ {2}x                   (\because \cot x = \frac {\cos x}{\sin x})
                                                                           R.H.S.

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