Question

Prove that ${\sin }^{2}A{\cot }^{2}A+{\cos }^{2}A{\tan }^{2}A=1$.

Answer 1

LHS$={\sin }^{2}A{\cot }^{2}A+{\cos }^{2}A{\tan }^{2}A$

$={\sin }^{2}A\times \frac{{\cos }^{2}A}{{\sin }^{2}A}+{\cos }^{2}A\times \frac{{\sin }^{2}A}{{\cos }^{2}A}$

$={\cos }^{2}A+{\sin }^{2}A$

$=1$

$=RHS$

Hence proved