Question

Prove that $cose{c}^6\theta =co{t}^6\theta +3co{t}^2\theta cose{c}^2\theta +1$

Answer 1

Identity : $cose{c}^2\theta -{\cot }^2\theta =1$

$LHS=cose{c}^6\theta$

$={(1+{\cot }^2\theta )}^3$

$=1+{\cot }^6\theta +\mathrm{3.1.}{\cot }^2\theta (1+{\cot }^2\theta )$

$={\cot }^6\theta +3{\cot }^2\theta cose{c}^2\theta +1$

$=RHS$

Hence proved