Question

Prove that $(\sec \theta +\cos \theta )(\sec \theta -\cos \theta )={\tan }^2\theta +{\sin }^2\theta$.

Answer 1

LHS$=(\sec \theta +\cos \theta )(\sec \theta -\cos \theta )$

$={\sec }^2\theta -{\cos }^2\theta$

$=(1+{\tan }^2\theta )-(1-{\sin }^2\theta )$

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

$=RHS$

Hence proved