Simplify the following expression to a single trigonometric function: sin񑥮sin(90° + 񑦩 − cos񑥮sin(180° + 񑦩 cos񑥮cos(񑦠− 360°) + sin(−񑥩sin?

Answer 1

cos(x) sin(90° + y) - sin(x) sin(180° + y) cos(x) cos(y - 360°) + sin(-x) sin(y)
Simplify using trigonometric identities:
cos(x) sin(90° + y) - sin(x) sin(180° + y) cos(x) cos(y) + sin(x) sin(y)
cos(x) cos(y) - sin(x) sin(y) - sin(x) cos(y) = cos(x) cos(y) - sin(x) sin(y) - sin(x) cos(y)
cos(x+y)
Therefore, the simplified expression is cos(x+y).