# Trigonometric problem

1. May 25, 2004

### Johnny Leong

How to solve: sin x + sin 3x + sin 2x = 1 + cos 2x + cos x, give general solution in radians for x.
How to get start?

2. May 25, 2004

### arildno

You will need the following identities:
$$\cos^{2}x+\sin^{2}x=1,\cos^{2}x-\sin^{2}x=\cos2x$$
$$\sin(a+b)=\sin(a)\cos(b)+\sin(b)\cos(a)$$

3. May 26, 2004

### Johnny Leong

I have solved the problem. I have used the identities:
sin x + sin y = 2 sin (x+y)/2 cos(x-y)/2 and cos 2x = 2 cos^2 (x) - 1.
With these two identities, it's easy to solve the problem.