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If { x } +{ }^{ 2 }x=1, then { }^{ 2 }x+{ }^{ 4 }x is :

Question

If $sin x + sin^{2} x = 1$ , then $cos^{2} x + cos^{4} x$ is :

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Levi Discussed

sin x + sin^{2} x = 1

, then

cos^{2} x + cos^{4} x

is :

9 mins ago

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9 mins ago

Text solutionVerified

Given,

sin x + sin^{2} x = 1

\Rightarrow sin x = 1 - sin^{2} x

\Rightarrow sin x = cos^{2} x

Then

sin^{2} x = cos^{4} x

\Rightarrow 1 - cos^{2} x = cos^{4} x

Therefore,

cos^{2} x + cos^{4} x = 1

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