Question

Sec^4-sec^2=tan^4+tan^2 Prove?

Answer 1

sec⁴x – sec²x = sec²x ( sec²x – 1)
= ( 1 + tan²x) tan²x
= tan²x + tan⁴x

Answer 2

Answer:

To Prove : $Sec^4x-sec^2x=tan^4x+tan^2x$

Solution :

$sec^4x- sec^4x$

Identity : $1+tan^a = sec^2 a$

$sec^2x ( sec^2x - 1)$

$( 1 + tan^2x) tan^2x$

$tan^2x + tan^2x$

$Sec^4x-sec^2x=tan^4x+tan^2x$

Hence proved