Derive the formula to find the angle between two lines with slopes `m_(1) and m_(2)`

Derive a formula for the angle between two lines with slopes m_(1) and m_(2) . Hence the slopes of the lines which make an angle pi/4 with the line x-2y+5=0

Derive a formula for the angle between two lines with slope m1 and m2.Hence find the acute angle between the lines sqrt 3x+y=1 and x+sqrt3 y=1 .

Find the angle between the lines whose slopes are -3 and -1/(2) .

Find the angle between the lines whose slope are (1)/(2) and 3.

Find the angle between the line whose slope are 2 and -1 .

State True or False: Acute angle between two lines with slopes m and m_(2) is given by tantheta=|(m_(2)-m_(1))/(1+m_(1)m_(2))|

A : If the angle between the lines kx-y+6=0, 3x+5y+7=0 is pi//4 one value of k is 4 R : If theta is angle between the lines with slopes m_(1), m_(2) then tan theta=(|m_(1)-m_(2)|)/(|1+m_(1)m_(2)|) .

Find the equations of the bisectors of the angles, between the lines through (0,0) with slopes 1 and 2 .