SOLUTION: Simplify the following expressions as much as possible. cos(x+y)-cos(x-y)

Algebra ->  Trigonometry-basics -> SOLUTION: Simplify the following expressions as much as possible. cos(x+y)-cos(x-y)      Log On


   

Question 1138452: Simplify the following expressions as much as possible.
cos(x+y)-cos(x-y)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Use these two identities
cos%28x%2By%29+=+cos%28x%29cos%28y%29+-+sin%28x%29sin%28y%29
cos%28x-y%29+=+cos%28x%29cos%28y%29+%2B+sin%28x%29sin%28y%29

to say that,






cos%28x%2By%29+-+cos%28x-y%29+=+%280%29+%2B+%28-2sin%28x%29sin%28y%29%29

cos%28x%2By%29+-+cos%28x-y%29+=+-2sin%28x%29sin%28y%29

The original expression simplifies to -2sin(x)sin(y)

cos%28x%2By%29+-+cos%28x-y%29+=+-2sin%28x%29sin%28y%29 is an identity. It is a true equation no matter what values of x and y you select.