Q60 / 160 · AP EAMCET 2018 (23 Apr Shift 2) · Mathematics
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$225^{\circ}$
- Correct answerD$250^{\circ}$
Solution
$$
\begin{gathered}
\text { If } \tan \theta=\frac{\cos 25^{\circ}+\sin 25^{\circ}}{\cos 25^{\circ}-\sin 25^{\circ}}=\frac{1+\tan 25^{\circ}}{1-\tan 25^{\circ}} \\
=\tan \left(45^{\circ}+25^{\circ}\right)
\end{gathered}
$$
$\because \theta$ is in the third quadrant, so
$$
\begin{aligned}
& \tan \theta=\tan 70^{\circ}=\tan \left(180^{\circ}+70^{\circ}\right)=\tan 250^{\circ} \\
& \Rightarrow \quad \theta=250^{\circ} \text {. } \\
&
\end{aligned}
$$
Hence, the correct answer is option: 'D'.