Question

If $\tan \, \theta = \frac{\cos 25^{\circ} + \sin 25^{\circ} }{\cos 25^{\circ} - \sin 25^{\circ} }$ and $\theta$ is in the third quadrant, then $\theta = $

• A. $200^{\circ}$
• B. $205^{\circ}$
• C. $225^{\circ}$
• D. $250^{\circ}$

Answer 1

The Correct Option is D

If $\tan \theta=\frac{\cos 25^{\circ}+\sin 25^{\circ}}{\cos 25^{\circ}-\sin 25^{\circ}}=\frac{1+\tan 25^{\circ}}{1-\tan 25^{\circ}}$ $=\tan \left(45^{\circ}+25^{\circ}\right)$ $\because \theta$ is in the third quadrant, so $\tan \theta=\tan 70^{\circ}=\tan \left(180^{\circ}+70^{\circ}\right)=\tan 250^{\circ}$ $\Rightarrow \theta=250^{\circ} .$