Question

If $sin\theta +cosec\theta =2$ then ${sin}^2\theta +{cosec}^2\theta$ is equal to

• A. $1$
• B. $4$
• C. $2$
• D. none

Answer 1

Answer: (C)

$2$

$\sin \theta +\csc \theta =2$

$\Rightarrow \sin \theta +\frac{1}{\sin \theta }=2$

$\Rightarrow {\sin }^2\theta -2\sin \theta +1=0$

$\Rightarrow (\sin \theta -1{)}^2=0$

$\Rightarrow \sin \theta =1$

$\Rightarrow {\sin }^2\theta +{\csc }^2\theta ={\sin }^2\theta +\frac{1}{{\sin }^2\theta }$

$=1+1$

$=2$