Question

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

Answer 1

L.H.S$={\cos }^2\theta +\frac{1}{1+{\cot }^2\theta }$

$={\cos }^2\theta +\frac{1}{{\csc }^2\theta }$

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

$=1=$R.H.S

Hence proved.