Prove that:
$sin^{4} θ - cos^{4} θ = 1 - 2 cos^{2} θ$

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Prove that:

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

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Text solutionVerified

sin^{4} θ - cos^{4} θ

= (sin^{2} θ)^{2} - (cos^{2} θ)^{2}

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

= (sin^{2} θ - cos^{2} θ)

= 1 - cos^{2} θ - cos^{2} θ

= 1 - 2 cos^{2} θ

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