Question

If $\sec \theta =\sqrt{2}$ for $\theta \in [0,\pi ];\theta \ne \frac{\pi }{2}$ , then the value of $\sin 2\theta$ is :

• A. $\frac{\sqrt{3}}{2}$
• B. $1$
• C. $0.5$
• D. $0$

Answer 1

The correct option is B $1$

$\text{For}\sec \theta =\sqrt{2}\text{, where}\theta \in [0,\pi ]-\left\{\frac{\pi }{2}\right\}$
$\Rightarrow \theta$ is ${45}^{\circ }$.
$\therefore 2\theta$ is ${90}^{\circ }$.
$\Rightarrow \sin 2\theta =\sin {90}^{\circ }=1$