Question

cosec^6a=cot^6A+1+3cot^2A.cosec^2A

Answer 1

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)],

⇒csc6θ=cot6θ+3cot2θcsc2θ+1.

Answer 2

Solution to your question