Question

If $\sin \theta +cosec\theta =2$ then find the value of ${\sin }^2\theta +{cosec}^2\theta$

Answer 1

$\sin \theta +cosec\theta =2$

$\Rightarrow {(\sin \theta +cosec\theta )}^2=4$

$\Rightarrow {\sin }^2\theta +{cosec}^2\theta +2\sin \theta cosec\theta =4$

$\Rightarrow {\sin }^2\theta +{cosec}^2\theta +2=4$ since $\sin \theta cosec\theta =1$

$\Rightarrow {\sin }^2\theta +{cosec}^2\theta =4-2$

$\therefore {\sin }^2\theta +{cosec}^2\theta =2$