Question

Prove:

$\frac{{\tan }^2\theta }{1+{\tan }^2\theta }+\frac{{\cot }^2\theta }{1+{\cot }^2\theta }=1$

Answer 1

$\frac{{\tan }^2\theta }{1+{\tan }^2\theta }+\frac{{\cot }^2\theta }{1+{\cot }^2\theta }$

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

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

$=1$