Question

please if know the perfect answer then only give the answer .........​

Answer 1

Step-by-step explanation:

We know that,

Cosec²θ = Cot²θ + 1

Cubing both sides we get,

(Cosec²θ)³ = (Cot²θ + 1)³

Using the identity,

(x + y)³ = x³ + 3xy(x + y) + y³

Thus,

Cosec⁶θ = (Cot²θ)³ + 3(Cot²θ)(1)(Cot²θ + 1) + 1³

Cosec⁶θ = Cot⁶θ + 3Cot²θ(Cot²θ + 1) + 1

Now, we know that, Cosec²θ = Cot²θ + 1

So,

Cosec⁶θ = Cot⁶θ + 3Cot²θCosec²θ + 1

Hence,

Cosec⁶θ = 1 + 3Cot²θCosec²θ + Cot⁶θ

Hence proved,

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