Two lines $$L_1$$ and $$L_2$$ make intercepts a. —b and b, —a respectively on the x and y axes. Then angle between $$L_1$$ and $$L_2$$ is

we know the line fourmula  y = mx + c

we have two line equation 

ax - yb = 0 and bx - ay = 0 

then we get 

$$y_{1}$$ = $$m_{1}$$x + $$ c_{1}$$          and         $$y_{2}$$ = $$m_{2}$$x + $$ c_{2}$$ 

put the value of x and y  

we get

-b = a$$m_{1}$$ + $$ c_{1}$$                  and           -a = b $$m_{2}$$  +   $$ c_{2}$$ 

where   $$ c_{1}$$ and   $$ c_{2}$$ are constant  = 0 then 

$$m_{1}$$ = -b\a                                  and            $$m_{2}$$ = -a\b 

then we know that the angle is 

$$\tan\theta$$ = |$$\frac {(m_{1}-m_{2})}{(1 +m_{1}m_{2})}$$ | 

put the value of $$m_{1}$$ and $$m_{2}$$ we get 

$$\tan\theta$$ = $$\frac {(a^{2}-b^{2})}{2ab}$$  Answer