Question

tan^4o + tan^2o = sec^2o-sec^2o​

Answer 1

Correct question is tan⁴x + tan²x = sec⁴x - sec²x

Proof:-

RHS = sec⁴x - sec²x

= 1/cos⁴x - 1/cos²x

= 1- cos²x / cos⁴x

= sin²x / cos⁴x

= tan²x ( 1/cos²x )

Applying the trigonometric identity :- (1/cos²x) = (1+ tan²x)....... (1)

We get :-

= tan²x (1+ tan²x) ......... [from eq. - (1)]

= tan⁴x + tan²x = LHS..

Hence, RHS = LHS

Hope it will help you....