Question

Prove the identity $\frac{\cos \alpha}{\sin \alpha} \cdot \frac{1}{\cos ^{2} \alpha} \cdot \sin ^{2} \alpha=\tan \alpha$

Answer 1

$\frac{\cos \alpha}{\sin \alpha} \cdot \frac{1}{\cos ^{2} \alpha} \cdot \sin ^{2} \alpha=\tan \alpha$

LHS :
$\frac{\cos \alpha}{\sin \alpha} \cdot \frac{1}{\cos \alpha} \cdot \frac{1}{\cos \alpha} \cdot \sin \alpha \cdot \sin \alpha$
$=\frac{\sin \alpha}{\cos \alpha}$
$=\tan \alpha$
$L H S=R H S$