Question

Sec^4theta - sec^2theta=tan^2theta + tan^4theta

Answer 1

= sec^{2}\theta(sec^{2}\theta-1)sec

2

θ(sec

2

θ−1)

= (1+tan^{2}\theta)(1+tan^{2}\theta-1)(1+tan

2

θ)(1+tan

2

θ−1)

/* By Trigonometric identity:

sec²A = 1+tan²A */

= (1+tan^{2}\theta)\times tan^{2}\theta(1+tan

2

θ)×tan

2

θ

=tan^{2}\theta+tan^{4}\thetatan

2

θ+tan

4

θ

Rearranging the terms, we get

= tan^{4}\theta+tan^{2}\thetatan

4

θ+tan

2

θ

= RHS

Answer 2

Formula used :

${sec}^{2} \: \theta = (1 + {tan}^{2} \: \theta) \\ {tan}^{2} \: \theta = {sec}^{2} \: \theta - 1$

Refer the attachment for complete answer ✔️