Question

Prove that.........cosec^6 x - cot^6 x = 3cot^2x cosec^2x+1

Answer 1

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Answer 2

We know that, csc2θ=cot2θ+1.......(1).

(csc2θ)3=(cot2θ+1)3.

Since, (x+y)3=x3+y3+3xy(x+y), we have,

csc6θ=(cot2θ)3+13+3(cot2θ)(1)(cot2θ+1),

=cot6θ+1+3cot2θ(csc2θ).......[∵,(1)],