sin x + sin y = ½ dan cos x +cos y =⅓ hitung sin (x-y)

jawab

(sin x + sin y)² + (cos x + cos y)² = (1/2)² +(1/3)²
sin² x + sin² y + 2 sin x sin y +cos² x + cos² y + 2 cos x cos y = 1/4 + 1/9
(sin² x + cos² x) + (sin² y+ cos² y) + 2 ( sin x sin y + cos x cos y) = 13/36
(1) + (1) + 2 { cos (x -y)} = 13/36
2 cos (x-y) = 13/36 - 2  = - 59/36
cos (x-y)= -59/72
sin (x-y) = √ { 1 - cos² (x-y)} = √(1 - (-59/72)² = 0, 57