Question

proove

$(\sec A+\cos A)(\sec A-\cos A)={\tan }^{2}A+{\sin }^{2}A$

Answer 1

$(\sec A+\cos A)(\sec A-\cos A)$

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

$=1+{\tan }^{2}A-1+{\sin }^{2}A={\tan }^{2}A+{\sin }^{2}A$