Question

Express cos(3x)sin(3x) in terms of sin(x) and cos(x).

A) 3/2 sin(x)cos(x)
B) 1/2 sin(x)cos(x)
C) 2sin(x)cos(x)
D) 1/4 sin(x)cos(x)

Answer 1

To express cos(3x)sin(3x) in terms of sin(x) and cos(x), we can use the double angle formula for sine: sin(2theta) = 2sin(theta)cos(theta). Applying this formula, we have: cos(3x)sin(3x) = sin(2(3x)) = 2sin(3x)cos(3x). Therefore, the expression cos(3x)sin(3x) can be written as 2sin(3x)cos(3x).

Step-by-step explanation:

To express cos(3x)sin(3x) in terms of sin(x) and cos(x), we can use the double angle formula for sine: sin(2theta) = 2sin(theta)cos(theta). Applying this formula, we have:

cos(3x)sin(3x) = sin(2(3x)) = 2sin(3x)cos(3x).

Therefore, the expression cos(3x)sin(3x) can be written as 2sin(3x)cos(3x).