Question

How to prove sec^4A-sec^2A=tan^4A+tan^2A

Answer 1

Use the identities,

$\sec^2 A=1+\tan ^2 A$.

$(a+b)^2=a^2+2ab+b^2$

Here,

$LHS=\sec^4 A-\sec^2 A=(1+\tan ^2 A)^2-1-\tan ^2 A\\ LHS=\sec^4 A-\sec^2 A=\tan^4 A+2\tan^2 A+1-1-\tan ^2 A\\ LHS=\sec^4 A-\sec^2 A=\tan^4 A+\tan^2 A=RHS$

The proof is complete.