Question 253255
You have the right start. 
(sinx cosy  + sinycosx)(sinxcosy - sinycosx) which is difference of 2 squares so
(sin^2 x cos^2 y)- (sin^2 y cos^2 x) when multiplied out
Now sin^2 = 1 - cos^2 so, rewriting
cos^2 y ( 1 - cos^2 x) - cos^2 x (1 - cos^2 y) and expanding
cos^2 y - cos^2 y cos^2 x - cos^2 x + cos^2 x cos^2 y then adding up
cos^2 y - cos^2 x