Question

4 sinx sin(pi/3+x) sin(2 pi/3+x) = sin3x ?
?

Answer 1

\[π = 180\]
So,

Answer 2

Lets convert radians to degrees.
4 sinx sin(pi/3+x) sin(2 pi/3+x) = sin3x
4 sinx sin(60+x) sin(120+x) = sin3x

sin(60 + x) = sin(60)cos(x) + cos(60)sin(x)
sin(120 + x) = sin(120)cos(x) + cos(120)sin(x)

So we have so far, (I'm assuming it's 4sinx times...since there is no plus symbol)
4 sinx (sin(120)cos(x) + cos(120)sin(x) + sin(60)cos(x) + cos(60)sin(x))= sin3x) = sin3x
sin(120)cos(x) + cos(120)sin(x) + sin(60)cos(x) + cos(60)sin(x))= sin3x= sin3x / 4sinx

Answer 3

\[Sin120=Sin60=\frac{\sqrt{3}}{2}\]\[Cos120=-\frac{1}{2}\]\[Cos60=\frac{1}{2}\]

Answer 4

In my second comment, ignore at the end where it says "=sin(3x)" the first time