write sin4xcos2 as the sum or difference of two functions. answers: 1/2(cos6x+cos2x), 1/2(cos2x-cos6x), 1/2(sin6x+sin2x), sin6x-sin2x
To write sin(4x)cos(2x) as the sum or difference of two functions, we can make use of the product-to-sum identities. One such identity states that sin(A)cos(B) = 1/2 [sin(A + B) + sin(A - B)].
In this case, we have sin(4x)cos(2x). So, we can express this as:
1/2 [sin(4x + 2x) + sin(4x - 2x)]
Simplifying this expression, we get:
1/2 [sin(6x) + sin(2x)]
Therefore, the sum of two functions that is equivalent to sin(4x)cos(2x) is 1/2 [sin(6x) + sin(2x)].