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Which of the following expressions is equal to 1 – cos4 θ?

Which of the following expressions is equal to 1 – cos4 θ?-example-1
User Zarel
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1 Answer

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1-\cos^4\left(θ\right)=(1-\cos^2\left(θ\right))(1+\cos^2\left(θ\right))

Given that: sin^2 θ = 1 - cos^2 θ, then


1-\cos^4\left(θ\right)=(1+\cos^2\left(θ\right))\sin^2\left(θ\right)=\sin^2\left(θ\right)+\sin^2\left(θ\right)\cos^2\left(θ\right)
1-\cos^4\left(θ\right)=(1+\cos^2\left(θ\right))\sin^2\left(θ\right)=\sin^2\left(θ\right)+\sin^2\lparenθ)(1-\sin^2\lparenθ))
1-\cos^4\left(θ\right)=\sin^2\left(θ\right)+\sin^2\lparenθ)(1-\sin^2\lparenθ))=\sin^2\left(θ\right)+\sin^2\lparenθ)-\sin^4\lparenθ)=2\sin^2-\sin^4\lparenθ)
1-\cos^4\left(θ\right)=2\sin^2-\sin^4\lparenθ)

So the answer is the first option.

User Reagan
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