Question

cosec^6x-cot^6x=3cot^2xcosec^2x+1

Answer 1

To prove: 
Cosec^6x = cot^6x + 1 + 3cot^2x.coscec^2x
R.H.S = cot^6x + 1 + 3cot^2x.coscec^2x
=(cot^2x)^3 + (cosec^2x - cot^2x)^3 + 3.cot^2x.(cosec^2x - cot^2x).{cot^2x + (cosec^2x - cot^2x)} 
(Since cosec^2x - cot^2x = 1) 
={cot^2x + (cosec^2x - cot^2x}^3 
={cosec^2x}^3 
=cosec^6x = L.H.S(Proved)