We know that the equation of two straight lines which passes through a point (x1,y1) and made a given angle α with the given straight line y=mx+c are y−y1=‌
m±tan‌α
1∓m‌tan‌α
(x−x1) Here, x1=1,y1=1,α=60∘ andm=−1 (slope of line x+y−3=0 ) So, equation of lines are y−1=‌
−1−tan‌60∘
1+(−1)‌tan‌60∘
(x−1) and ‌‌y−1=‌
−1+tan‌60∘
1−(−1)‌tan‌60∘
(x−1) ⇒‌‌y−1=‌
−1−√3
1−√3
(x−1) and ‌‌y−1=‌
−1+√3
1+√3
(x−1) ⇒‌‌(y−1)(1−√3)=(−1−√3)(x−1) and (y−1)(1+√3)=(−1+√3)(x−1)⇒‌‌(1+√3)x+(1−√3)y−1+√3−1−√3=0 and (1−√3)x+(1+√3)y−1−√3−1+√3=0 ⇒‌‌(1+√3)x+(1−√3)y−2=0 and (1+√3)x+(1−√3)y−2=0