Question:
Prove that. \(\frac{cos(π+x)cos(-x)}{sin(π-x)cos(\frac{π}{2}+x)}=cot^2x\)
Prove that. \(\frac{cos(π+x)cos(-x)}{sin(π-x)cos(\frac{π}{2}+x)}=cot^2x\)
Updated On: Oct 19, 2023
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Solution and Explanation
\(L.H.S=\frac{cos({\pi}+x)cos(-x)}{sin({\pi}-x)cos(\frac{\pi}{2}+x)}\)
\(=\frac{[-cos\,x][cos\,x]}{(sin\,x)(-sin\,x)}\)
\(\frac{-cos^2x}{-sin^2x}\)
\(=cot^2x\)
\(=R.H.S.\)
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