write sin4xcos2 as the sum or difference of two functions.
To write sin(4x)cos(2x) as the sum or difference of two functions, we can use the trigonometric identity:
sin(A)cos(B) = (1/2)[sin(A + B) + sin(A - B)]
Applying this identity to sin(4x)cos(2x), we have:
sin(4x)cos(2x) = (1/2)[sin(4x + 2x) + sin(4x - 2x)]
Simplifying inside the brackets:
= (1/2)[sin(6x) + sin(2x)]
Therefore, sin(4x)cos(2x) can be written as the sum of sin(6x) and sin(2x).