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Maharashtra State BoardSSC (English Medium) 10th Standard

If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1

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Question

If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1

Sum
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Solution

sin θ + sin2 θ = 1 ......[Given]

∴ sin θ = 1 − sin2 θ

∴ sin θ = cos2 θ ......[∵ 1 − sin2 θ = cos2 θ]

∴ sin2 θ = cos4 θ ......[Squaring both the sides]

∴ 1 − cos2 θ = cos4 θ ......[∵ sin2 θ = 1 − cos2 θ]

∴ 1 = cos2 θ + cos4 θ

∴ cos2 θ + cos4 θ = 1

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