Question

If $\text{cosec}\theta =\frac{3}{2}$, then find the value of $2({\text{cosec}}^2\theta +{\cot }^2\theta )$.

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is D $7$

$cosec\theta =\left(\frac{3}{2}\right)\therefore 2(cose{c}^2\theta +co{t}^2\theta )=2[cose{c}^2\theta +cose{c}^2\theta -1]=2[2\times (\frac{3}{2}{)}^2-1-1]=2[2\times (\frac{9}{4})-1]=2\left(\right(\frac{9}{2})-1)=2\times \left(\frac{7}{2}\right)=7$