Question

prove that : tan⁴+tan²=sec⁴-sec²prove that​

Answer 1

Answer:

Proof of tan^4 x + tan^2 x = sec^4 x - sec^2 x.

LHS = tan^4 x + tan^2 x

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

= tan^2 x *sec ^2 x. [Because tan^2 x + 1 = sec ^2 x]

= (sec^2 x -1)*sec^2 x

= sec^4 x - sec^2 x = RHS. Proved.

Answer 2

Given :

sec⁴ θ – sec²θ = tan⁴θ + tan²θ

L.H.S

= sec⁴ θ – sec²θ

= sec² θ (sec² θ -1)

= (1 + tan² θ) (1 + tan² θ -1) …..[ sec² θ = 1 + tan² θ ]

= (1 + tan² θ) ( tan² θ)

= tan²θ + tan⁴θ

L.H.S = R.H.S

I hope you got your answer…