If the angle between two lines is $\frac{\pi}{4}$ and the slope of one of the lines is $\frac{1}{2}$, then the slope of other line will be

Answer : Option C

Explanation :

Here, $\theta=\frac{\pi}{4}$ $m_{1}=m$ $m_{2}=\frac{1}{2}$ We know that $\tan \theta=\left|\frac{m_{1}-m_{2}}{1+m_{1} m_{2}}\right|$ $\tan \frac{\pi}{4}=\left|\frac{m-\frac{1}{2}}{1+\frac{m}{2}}\right|$ $\Rightarrow 1=\frac{2 m-1}{2+m}$ $\Rightarrow 2+m=2 m-1$