Question

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

• 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. $\sin 135^{\circ }$