Q:

Find angle between two lines by given equations

I have equations: $3x + y - 2 = 0$ and $4x - 2y + 5 = 0$. My target is to find angle. 
I have used formula: $\tan\theta= \frac{m2-m1}{1 + |m2||m1|}$
First I convert equations: 
$y = -3x - 2$ and 
$-2y = -4x + 5$ => 
$-y = 2x + \frac{5}{2}$ => 
$y = -2x - \frac{5}{2}$
Now I got: $\tan\theta= \frac{-2-3}{1+-2.(3)}$, which will result of $\frac{-5}{-5}$, which in angles is 57.29°, but the right answer is: $\frac{\pi}{4}$. Where is my mistake. Please explain. Thank you.

A:

Its easy..You have almost solved it .
You have already shown $\tan(\theta)= -5/-5= 1$
All that remains is to find a special value of theta to satisfy the equation..
taking $\arctan$ on both sides...One finds the answer to be $\pi/4$...
$$\sin(\pi/4)=\cos(\pi/4)$$
$$\tan(\pi/4)=1.$$

