Solve the problem

Question

Sin(6x)-sin(3x)

you need to answer as a product of sine or cosine function.

Answer 1

Notice that you can write 3x and 6x in the following ways

6x = (9/2)x + (3/2)x

3x = (9/2)x - (3/2)x

You can find these fractional coefficients by solving the following equations

a + b = 6

a - b = 3

After that, you can use this Trig. formula to simplify the expression,

cos(a)sin(b) = (1/2)(sin(a+b)-sin(a-b))