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

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\(sinθ+sin^2⁡θ=1 \)
বা, \(sinθ=1-sin^2⁡θ \)
বা, \(sinθ=cos^2⁡θ \)
বা, \(cos^2⁡θ=sinθ\)

\(∴ cos^2⁡θ+cos^4⁡θ\)
\(=cos^2⁡θ+(cos^2⁡θ )^2 \)
\(=cos^2⁡θ+(sinθ)^2\) [\(cos^2⁡θ=sinθ\) বসিয়ে ]
\(=cos^2⁡θ+sin^2⁡θ\)
\(=1\) (প্রমাণিত)