Question

cos(2x+4h)-cos(2x+2h)=?

Answer 1

[AI-generated answer — Explain Bot]

To simplify the expression cos(2x+4h) - cos(2x+2h), we can make use of the trigonometric identity:

cos(A) - cos(B) = -2 sin((A+B)/2) sin((A-B)/2)

In our case, A = 2x+4h and B = 2x+2h. Plugging in these values, we get:

cos(2x+4h) - cos(2x+2h) = -2 sin((2x+4h+2x+2h)/2) sin((2x+4h-2x-2h)/2)

Simplifying inside the sine function:

cos(2x+4h) - cos(2x+2h) = -2 sin((4x+6h)/2) sin((2h)/2)

cos(2x+4h) - cos(2x+2h) = -2 sin(2x+3h) sin(h)

Thus, the simplified form of cos(2x+4h) - cos(2x+2h) is -2 sin(2x+3h) sin(h).