If $\tan \theta=\frac{\cos 25^{\circ}+\sin 25^{\circ}}{\cos 25^{\circ}-\sin 25^{\circ}}$ and $\theta$ is in…
If $\tan \theta=\frac{\cos 25^{\circ}+\sin 25^{\circ}}{\cos 25^{\circ}-\sin 25^{\circ}}$ and $\theta$ is in the third quadrant, then $\theta=$
- $200^{\circ}$
- $205^{\circ}$
- $225^{\circ}$
- $250^{\circ}$
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}
$
Asked in: AP EAMCET 2018 (23 Apr Shift 2)
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