Question

Prove the following trigonometric identities:
cosec6θ=cot6θ+3cot²θcosec²θ+1

Answer 1

Answer:

$\csc(60 = \cot(60 + 3$

Answer 2

cosec^6θ = cot^6θ + 3Cosec²θ.Cot²θ + 1  proved

Step-by-step explanation:

To prove: cosec^6θ = cot^6θ + 3cot²θ cosec²θ + 1

Proof:  

We know Cosec²θ - Cot²θ = 1

Cubing both sides of the above, we get:

(Cosec²θ - Cot²θ)³  = 1

cosec^6θ - cot^6θ -3Cosec²θ.Cot²θ(Cosec²θ - Cot²θ) = 1 [from a³ -b³ = (a+b) (a² + ab + b²) ]

cosec^6θ - cot^6θ -3Cosec²θ.Cot²θ (1) = 1

cosec^6θ - cot^6θ -3Cosec²θ.Cot²θ = 1

 cosec^6θ = cot^6θ + 3Cosec²θ.Cot²θ + 1

Hence proved.