cosec6θ = Cot6θ + 3Cot2θCosec2θ + 1
cosec6θ - Cot6θ - 3Cot2θCosec2θ = 1 ........(i)
since we know that
(a - b)3 = a3 - b3 - 3ab(a-b)
so we can write LHS of eq. (i) as
(cosec2θ)3 - (Cot2θ)3 - 3cot2θcosec2θ(cosec2θ - cot2θ) ...... ( cosec2θ - cot2θ = 1)
= (cosec2θ - cot2θ)3
= 1 = RHS
Hence proved
