Question

70) Prove that tan4 theta + tan2 theta= sec4 theta - sec2 theta

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Answer 1

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Answer 2

$tan^4\ \theta + tan^2\ \theta = sec^4\ \theta -sec^2\ \theta$

Solution:

Given that,

We have to prove:

$tan^4\ \theta + tan^2\ \theta = sec^4\ \theta -sec^2\ \theta$

Take the LHS

$tan^4\ \theta + tan^2\ \theta$

$Take\ tan^2\ \theta\ as\ common$

$tan^2\theta(1+tan^2\ \theta)$ ---------- (1 )

We know that,

$1+tan^2\ \theta = sec^2\ \theta$

Therefore, ( 1 ) becomes,

$(sec^2 \theta - 1)(sec^2 \theta)$

$sec^4\ \theta - sec^2 \theta$

Thus,

LHS = RHS

Thus proved

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