# 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

8 years ago
$(0,0), (a,0),(acos\alpha ,asin\alpha ),((1+cos\alpha )a),asin\alpha )$,

$first, diagonal, will ,pass thorough,{ (0,0), ((1+cos\alpha )a),asin\alpha )}$

$second, diagonal, will ,pass thorough, (a,0),(acos\alpha ,asin\alpha )$
just find equation of digonls using two points.