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

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Solve

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

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Text solutionVerified

L . H . S = cos^{4} θ + sin^{4} θ

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

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

= 1 - 2 sin^{2} θ cos^{2} θ [∵ sin^{2} θ + cos^{2} θ = 1]

= R . H . S

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