If sin theta + sin² theta = 1, prove that cos² theta + cos⁴ theta = 1
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Step-by-step explanation:
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Step-by-step explanation:
Given, sinθ+sin²θ=1
⇒sinθ=1−sin² θ=cos²θ
Therefore, cos²θ+cos⁴ θ=cos²θ(1+cos²θ)
=sinθ(1+sinθ)
=sinθ+sin²θ
=1. ( ∵ given sinθ+sin²θ=1)
Hence proved
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