cos(2x+4h)-cos(2x+2h)
To simplify the expression cos(2x+4h) - cos(2x+2h), we can start by using the formula for the difference of two cosines.
The formula states:
cos(a) - cos(b) = -2sin((a+b)/2)sin((a-b)/2)
Comparing this formula with our expression, we have a = 2x+4h and b = 2x+2h.
So, let's substitute these values into the formula:
cos(2x+4h) - cos(2x+2h) = -2sin((2x+4h+2x+2h)/2)sin((2x+4h-(2x+2h))/2)
Now, simplify the expression inside the sine functions:
= -2sin((4x+6h)/2)sin((2h)/2)
= -2sin(2x+3h)sin(h)
Hence, the simplified expression for cos(2x+4h) - cos(2x+2h) is -2sin(2x+3h)sin(h).