Question

If $sin\theta =\frac{1}{3}$ then find the value $\left\{2{\cot }^2\theta +2\right\}$

Answer 1

$2co{t}^2\theta +2=2(1+co{t}^2\theta )$

$=2cose{c}^2\theta$

Now $sin\theta =\frac{1}{3}$

$\therefore cosec\theta =3$

$\therefore 2cose{c}^2\theta =2(3{)}^2=2\times 9$