Question

Prove :

tan4θ + tan2θ  =  sec4θ - sec2θ

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Answer 1

Solution :

Let A = tan4θ + tan2θ and B = sec4θ + sec2θ.

A = tan4θ + tan2θ

A = tan2θ (tan2θ + 1)

We know that,

tan2θ = sec2θ - 1

tan2θ + 1 = sec2θ

Then,

A = (sec2θ - 1)(sec2θ)

A = sec4θ - sec2θ

A = B (Proved)