Question

Prove that cos(pie-x)cos(-x)/sin(pie-x) cos (pie/2+x)​

Answer 1

To prove:-

$\large\sf { \frac{ cos( \pi + x) \ cos(-x)}{ sin ( \pi - x) \ cos \big ( \frac{ \pi}{2} + x \big ) } = cot^{2} x}$

Proof:-

$\large\sf { \frac{ cos( \pi + x) \ cos(-x)}{ sin ( \pi - x) \ cos \big ( \frac{ \pi}{2} + x \big ) } }$

$\large\sf { = \frac{ [ - cos \ x][cos \ x]}{ ( sin \ x) ( - sin \ x)}}$

$\large\sf { = \frac{ - cos^{2} x}{ - sin^{2} x}}$

$\large\sf { = cot^{2} x}$