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Question
If cos A + cos2A = 1, then sin2A + sin4A = ?
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Solution
cos A + cos2A = 1 ...[Given]
∴ cos A = 1 – cos2A
∴ cos A = sin2A ...`[(∵ sin^2A + cos^2A = 1),(∴ 1 - cos^2A = sin^2A)]`
∴ cos2A = sin4A ...[Squaring both the sides]
∴ 1 – sin2A = sin4A
∴ 1 = sin4A + sin2A
∴ sin2A + sin4A = 1
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