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# Prove the Following Trigonometric Identities Cosec6θ = Cot6θ + 3 Cot2θ Cosec2θ + 1 - CBSE Class 10 - Mathematics

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#### Question

Prove the following trigonometric identities

cosec6θ = cot6θ + 3 cot2θ cosec2θ + 1

#### Solution

We need to prove cosec6θ = cot6θ + 3 cot2θ cosec2θ + 1

Solving the L.H.S, we get

cosec^6 theta = (cosec^2 theta)^3

= (1 + cot^2 theta)^3     .......(1 + cot^2 theta = cosec^2 theta)

Further using the identity (a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2  we get

(1 + cot^2 theta)^3 = 1 + cot^6 theta + 3(1)^2 (cot^2 theta) + 3(1) (cot^2 theta)^2

= 1 + cot^6 theta + 3 cot^2 theta + 3 cot^4 theta

= 1 + cot^6 theta + 3 cot^2 theta (1 + cot^2 theta)

= 1 + cot^6 theta + 3 cot^2 theta cosec^2 theta    (using 1 + cot^2 theta = cosec^2 theta)

Hence proved.

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Solution Prove the Following Trigonometric Identities Cosec6θ = Cot6θ + 3 Cot2θ Cosec2θ + 1 Concept: Trigonometric Identities.
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