Solving a Trigonometric Equation with Identities

[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?
Anyone could help me, please?

 

[arildno]

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

 

[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.