for angles greater than right angles

Let x = 120 , y = 150 ,

Now , sin120 = sin(180-60) = sin60 = root3 / 2

Similarly , sin150 = sin30 = 1/2

cos120 = cos(180-60) = -cos60 = -1/2

cos150 = -cos30 = -root3 / 2

 

So L.H.S becomes root3 / 2 * -root3 / 2 + 1/2 * -1/2 = -1

Similarly R.H.S. = sin(120+150) = sin270 = -1

This implies that the for all angles the condition holds.