Question

Prove that:

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

Answer 1

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

Hence proved