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प्रश्न
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
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उत्तर
We have,
sinθ + sin2 θ = 1
⇒ sinθ = 1 – sin2 θ
⇒ sin θ = cos2 θ ......[∵ sin2 θ + cos2 θ = 1]
(sinθ)2 = (cos2 θ)2
sin2 θ = cos4 θ
= cos2 θ + cos4 θ
= sin θ + sin2 θ
cos2 θ + cos4 θ = 1
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