Question

If $\sin \theta =1/3,$ find the value of $2{\cot }^2\theta +2$

Answer 1

Given $\sin \theta =1/3⟹\text{cosec}\theta =3$

$2{\cot }^2\theta +2=2(1+{\cot }^2\theta )=2{\text{cosec}}^2\theta =2\left(9\right)=18$