Question

If $\tan \alpha =\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }$ then $\sin \alpha$ is equal to

• A. $\pm \frac{\sin \theta +\cos \theta }{\sqrt{2}}$
• B. $\pm \frac{\sin \theta -\cos \theta }{\sqrt{2}}$
• C. $\pm \left(\sin \theta -\cos \theta \right)$
• D. None of these

Answer 1

The correct option is B $\pm \frac{\sin \theta -\cos \theta }{\sqrt{2}}$

$\tan \alpha =\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }$

$\sin \alpha =\frac{\sin \theta -\cos \theta }{\sqrt{{\sin }^2\theta +{\cos }^2\theta +{\sin }^2\theta +{\cos }^2\theta }}$

$\sin \alpha =\pm \frac{\sin \theta -\cos \theta }{\sqrt{2}}$

$B$ is correct