How do you solve Sin(x/3)cos(x/3) = (1/2)sin(2x/3)?

1 Answer
Jun 23, 2016

This is a true statement. It holds true for all values of x.

Explanation:

We can show that this is a true statement. Start by multiplying both sides of the equation by 2.

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

Notice that if we let theta=x/3 then this is the sine double-angle identity.

2sin(theta)cos(theta)=sin(2theta)

sin(2theta)=sin(2theta)