One side of a square makes an angle alpha with x-axis and one vertex of the square is at the origin, prove that equations of its diagonals are y(cos alpha - sin alpha) = x(sin alpha - cos alpha) and y(sin alpha + cos alpha) + x(cos alpha - sin alpha) = a

just find equation of digonls using two points.

Sher Mohammad,

B.Tech, IIT Delhi

we have ,  slope of OB =tan alpha(45 degree + alpha).  slope of AC = -cot (45 degree +alpha) => Slope of AC=(cos alpa-sin alpha)÷(cos alpha+sin alpha)=sin alpha-cos alpha ÷sin alpha + cos alpha.Thus the equation of AC is, y-a sin alpha= sin alpha-cos alpha÷sin alpha+ cos alpha × (x- a cos alpha) => – x (sin alpha – cos alpha) + y (sin alpha +cos alpha)= a => y (sin alpha+ cos alpha)+ x (cos alpha – sin alpha) = a. Proved