Simplify cos(x+y)-cos(x-y)
remember these?
http://www.sosmath.com/trig/prodform/prodform.html
cos(A+-B)=cosAcosB-+sinASinB
http://www.purplemath.com/modules/idents.htm
To simplify the expression cos(x+y) - cos(x-y), we can use the trigonometric identity called the difference of cosines.
The difference of cosines identity states that cos(A) - cos(B) = -2sin((A+B)/2)sin((A-B)/2).
Let's apply this identity to our expression by letting A = x+y and B = x-y:
cos(x+y) - cos(x-y) = -2sin((x+y + x-y)/2)sin((x+y - x+y)/2)
Simplifying the expression inside the sine function:
= -2sin(x)sin(y)
Therefore, the simplified expression for cos(x+y) - cos(x-y) is -2sin(x)sin(y).