Question

if sin thita + sin2theta = 1,show that cos2theta +cos4theta
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Answer 1

Given:

$\sin \theta + \sin^2 \theta = 1$

We have to show that:

$\cos^2 \theta + \cos^4 \theta = 1$

Solution:

$\sin \theta + \sin^2 \theta = 1$

⇒ $\sin \theta = 1- \sin^2 \theta$

⇒ $\sin \theta = \cos^2 \theta$

Squaring both sides, we get

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

⇒ $1-\cos^2 \theta = \cos^4 \theta$

⇒ $\cos^2 \theta + \cos^4 \theta = 1$, shown.

Thus, $\cos^2 \theta + \cos^4 \theta = 1$, shown.