Question

Prove that $(1+{\cot }^{2}A){\sin }^{2}A=1$.

Answer 1

Identity : $cose{c}^{2}A-{\cot }^{2}A=1$

LHS $=(1+{\cot }^{2}A){\sin }^{2}A$

$=cose{c}^{2}A\times {\sin }^{2}A$

$=\frac{1}{si{n}^{2}A}\times si{n}^{2}A$

$=1$

$=RHS$