Question

Solve
$(\frac{4}{{\sec }^2\theta }+\frac{1}{1+{\cot }^2\theta }+3{\sin }^2\theta )$

Answer 1

$(\frac{4}{{\text{sec}}^2\theta }+\frac{1}{1+{\cot }^2\theta }+3{\sin }^2\theta )=(4{\cos }^2\theta +\frac{1}{{\text{cosec}}^2\theta }+3{\sin }^2\theta )=(4{\cos }^2\theta +{\sin }^2\theta +3{\sin }^2\theta )=(4{\cos }^2\theta +4{\cos }^2\theta )$

$=4({\sin }^2\theta +{\cos }^2\theta )=4$