Question

show that tan⁴teta +tan² teta= sec⁴teta- sec² teta​

Answer 1

EXPLANATION.

⇒ tan⁴θ + tan²θ = sec⁴θ - sec²θ.

As we know that,

We can write equation as,

From R.H.S.

⇒ sec⁴θ - sec²θ.

⇒ sec²θ(sec²θ - 1).

As we know that,

Formula of :

⇒ 1 + tan²θ = sec²θ.

Put the value in the equation, we get.

⇒ (1 + tan²θ)(1 + tan²θ - 1).

⇒ (1 + tan²θ)(tan²θ).

⇒ tan²θ + tan⁴θ

Hence proved.

Method = 2.

From L.H.S.

⇒ tan⁴θ + tan²θ.

As we know that,

We can write equation as,

⇒ tan²θ(tan²θ + 1).

As we know that,

Formula of :

⇒ 1 + tan²θ = sec²θ.

⇒ tan²θ = sec²θ - 1.

Using this formula in equation, we get.

⇒ (sec²θ - 1)(sec²θ - 1 + 1).

⇒ (sec²θ - 1)(sec²θ).

⇒ sec⁴θ - sec²θ.

Hence proved.