Question

What is the value of $\theta$ if $\sin \theta =\cos \theta =\frac{\tan \theta }{\sqrt{2}}$?

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

Given, $\sin \theta =\cos \theta$
Now, $\tan \theta =\frac{\sin \theta }{\cos \theta }$
$=1$ .......[Since $\sin \theta =\cos \theta ]$
We know $\tan \theta =\tan 45$
Therefore $\theta =45$