Question

If $\csc \theta =3/2$ then find the value of $2({\csc }^2\theta +{\cot }^2\theta )$

Answer 1

We know that ,

$co{t}^2\theta =cose{c}^2\theta -1$

Substitute this in given eq. we get,

$2(cose{c}^2\theta +cose{c}^2\theta -1$)

$⟹2(2cose{c}^2\theta -1$)

$⟹2\left(\right(\frac{3}{2}{)}^2-1)$

$⟹2(\frac{9}{4}-1)$

$⟹\frac{5}{2}$