Question

Prove that

cosec^6x-cot^6x-3cosec^2x.cot^2x=1

Answer 1

Answer:

Step-by-step explanation:

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)