Question

The number of solutions of $sin^{2}\,\theta=\frac{1}{2}$ In $\left[0, \pi\right]$ is $\ldots\ldots$

• A. three
• B. four
• C. two
• D. one

Answer 1

Answer: (C)

We have, $\sin ^{2} \theta =\frac{1}{2}$
$\Rightarrow \sin \theta=\pm \frac{1}{\sqrt{2}}$
We know, $\theta \in[0, \pi] \sin \theta$ is positive
$\therefore \sin \theta=\sin 45^{\circ}, \sin \left(180^{\circ}-45^{\circ}\right)$
i.e. $\sin 135^{\circ}$