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^{6} -^{6} =1+3^{2} ^{2}

Question

$csc^{6} θ - cot^{6} θ = 1 + 3 csc^{2} θ cot^{2} θ$

True

False

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csc^{6} θ - cot^{6} θ = 1 + 3 csc^{2} θ cot^{2} θ

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Text solutionVerified

csc^{6} θ - cot^{6} θ = (csc^{2} θ)^{3} - (cot^{2} θ)^{3}

= (csc^{2} θ - cot^{2} θ) (csc^{4} θ + cot^{4} θ + csc^{2} θ cot^{2} θ)

= (1) ((csc^{2} θ)^{2} + (cot^{2} θ)^{2} - 2 csc^{2} θ cot^{2} θ + 3 csc^{2} θ cot^{2} θ)

= (csc^{2} - cot^{2} θ)^{2} + 3 csc^{2} θ cot^{2} θ

= 1 + 3 csc^{2} θ cot^{2} θ

So the relation is

True

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