Question

prove that cos power 4 theta minus cos square theta is equals to sin power 4 theta minus sin square theta

Answer 1

Answer:

please refer to the attachment

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Answer 2

$cos^4 \theta - cos^2 \theta = sin^4 \theta - sin^2 \theta$

Solution:

Given that,

We have to prove

$cos^4 \theta - cos^2 \theta = sin^4 \theta - sin^2 \theta$

Take the LHS

$cos^4 \theta - cos^2 \theta\\\\Take\ cos^2 \theta\ as\ common\\\\cos^4 \theta - cos^2 \theta = cos^2 \theta (cos^2 \theta-1) ---- eqn 1\\\\We\ know\ that\\\\cos^2 \theta - 1 = -sin^2 \theta\\\\Also\\\\cos^2 \theta = 1 - sin^2 \theta$

Substitute these in eqn 1

$cos^4 \theta - cos^2 \theta = (1-sin^2 \theta)(-sin^2 \theta)\\\\cos^4 \theta - cos^2 \theta = -sin^2 \theta + sin^4 \theta\\\\cos^4 \theta - cos^2 \theta = sin^4 \theta - sin^2 \theta$

Thus, L.H.S = R.H.S

Therefore, the given is proved

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