A line through the point A(2, 0), which makes an angle of 30∘ with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15∘. The equation of the straight line in the new position is
(2−√3)x−y−4+2√3=0
Let AB be the initial position of the line and AC be its new position.
Slope of the line
AC=tan 15∘=(2−√3)
∴ Equation of the line AC is
(y−0)=(2−√3)(x−2)or y=(2−√3)x−4+2√3or (2−√3)x−y−4+2√3=0