If sinθ + sin^2 θ = 1, prove that cos^2 θ + cos^4 θ = 1 - Mathematics

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Sum

If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1

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Solution

We have,

`sinθ + sin^2 θ = 1`

`⇒ sinθ = 1 – sin^2 θ`

`⇒ sinθ = cos^2 θ`

Now, `cos^2 θ + cos^4 θ = cos^2 θ + (cos^2 θ)^2`

`= cos^2 θ + sin^2 θ = 1`

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