If \(\sin\theta + \sin^2\theta = 1\), show that \(\cos^2\theta + \cos^4\theta = 1\).

Doubtly Asked 29 Oct 2026 Practice test ssc 10th Save WhatsApp Report

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\(\sin\theta + \sin^2\theta = 1\) \(\therefore \sin\theta = 1 - \sin^2\theta = \cos^2\theta\) ...(I)

Now \(\cos^2\theta + \cos^4\theta = \cos^2\theta + (\cos^2\theta)^2\)

\(= \sin\theta + \sin^2\theta\) (using (I))

\(= 1\) (given). Hence \(\cos^2\theta + \cos^4\theta = 1\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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