Question

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

Answer 1

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)`