The equation of the straight line which makes an angle of 15∘ with the positive direction of x-axis and cuts an intercept of length 4 on the negative direction of y-axis, is
The slope of the line = m = tan 15∘= tan (45∘–30∘)
=tan 45∘−tan 30∘1+tan 45∘.tan 30∘=1−1√31+1√3=(√3−1)23−1=4−2√32=2−√3
Also, the intercept on y-axis = c = –4
Therefore, the equation of the line is
y=(2−√3)x−4 or (2−√3)x−y−4=0