Cosec^6 theta=cot^6 theta+3cot^2 theta xxcosec^2theta+1---------(prove this)?

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Answer 1 · 2017-08-16T17:31:26

Refer to a Proof given in the Explanation.

We know that, #csc^2theta=cot^2theta+1.......(1).#

#(csc^2theta)^3=(cot^2theta+1)^3.#

Since, #(x+y)^3=x^3+y^3+3xy(x+y),# we have,

# csc^6theta=(cot^2theta)^3+1^3+3(cot^2theta)(1)(cot^2theta+1),#

#=cot^6theta+1+3cot^2theta(csc^2theta).......[because, (1)],#

# rArr csc^6theta=cot^6theta+3cot^2thetacsc^2theta+1.#

Hence, the Proof.