Prove the following identities:
$1 - 2 sin^{2} θ + sin^{4} θ = cos^{4} θ$

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Prove the following identities:

1 - 2 sin^{2} θ + sin^{4} θ = cos^{4} θ

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Text solutionVerified

Taking

L H S = 1 - 2 sin^{2} θ + sin^{4} θ

we know that

cos^{2} θ + sin^{2} θ = 1 \Rightarrow 1 - 2 sin^{2} θ + (sin^{2} θ)^{2} = 1 - 2 sin^{2} θ + (1 - cos^{2} θ)^{2}

= 1 - 2 sin^{2} θ + 1 + cos^{4} θ - 2 cos^{2} θ = 2 - 2 (cos^{2} θ + sin^{2} θ) + cos^{4} θ = 2 - 2 (1) + cos^{4} θ = cos^{4} θ = R H S

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Question Text	Prove the following identities: $1 - 2 sin^{2} θ + sin^{4} θ = cos^{4} θ$
Answer Type	Text solution:1
Upvotes	150