Question

cot^2 A-tan^2A = cosec^2A-sec^2A ........prove this!

Answer 1

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Answer 2

Solution :

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Given :

To Prove :

Cot² A - tan² A = cosec² A - Sec² A

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Proof :

We know that,

Cosec² A - Cot² A = 1

&

Sec² A - Tan² A = 1

Hence,.

LHS & RHS

⇒ Cot² A - tan² A = cosec² A - Sec² A

⇒ Cot² A - Cosec² A = - Sec² A + Tan² A

⇒ - (Cosec² A - Cot² A) = - (Sec² A - Tan² A)

⇒ - (1) = - (1)

⇒ -1 = -1

⇒ LHS = RHS

∴ Hence proved,.

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