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# If $\sin \theta+cosec\theta=2$,then $\sin^2\theta+cosec^2\theta$ is equal to

$\begin{array}{1 1}(A)\;1&(B)\;4\\(C)\;2&(D)\;\text{None of these}\end{array}$

Toolbox:
• $cosec\theta=\large\frac{1}{\sin \theta}$
$\sin \theta+cosec\theta=2$
Squaring both side
$(\sin \theta+cosec\theta)^2=4$
$\sin^2\theta+cosec^2\theta+2\sin\theta cosec\theta=4$
$\sin^2\theta+cosec^2\theta+2\sin \theta\large\frac{1}{\sin \theta}$$=4$
$\sin^2\theta+cosec^2\theta+2=4$
$\sin^2\theta+cosec^2\theta=2$
Hence (C) is the correct answer.