# Prove that (Sin A+ sec A ) 2 + (Cos A + Cosec A)2  = ( 1 + Sec A . Cosec A ) 2

$\text{LHS }= 1+\dfrac1{\cos^2A}+\dfrac1{\sin^2A}+\dfrac{2\sin A}{\cos A}+\dfrac{2\cos A}{\sin A}\\ =1+\dfrac1{\cos^2A\sin^2A}+\dfrac2{\cos A\sin A}$