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Prove that ^{ 4 }{ } - ^{ 2 }{ } = ^{ 4 }{ } + ^{ 2 }{

Question

Prove that $csc^{4} θ - csc^{2} θ = cot^{4} θ + cot^{2} θ$

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Prove that

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

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Text solutionVerified

L . H . S = csc^{4} θ - csc^{2} θ

= (csc^{2} θ) - csc^{2} θ

= (1 + cot^{2} θ)^{2} - csc^{2} θ

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

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

= 2 cot^{2} θ - cot^{2} θ + cot^{4} θ

= cot^{2} θ + cot^{4} θ = r . h . s

proved.

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Question Text	Prove that $csc^{4} θ - csc^{2} θ = cot^{4} θ + cot^{2} θ$
Answer Type	Text solution:1
Upvotes	150