Question

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

Answer 1

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

${\cos }^{2}A+{\sin }^{2}A=1$

LHS = ${\cos }^{2}A+\frac{1}{1+{\cot }^{2}A}$

$={\cos }^{2}A+\frac{1}{cose{c}^{2}A}$

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

$=1$

$=RHS$

Hence proved