Combining Sine Functions: Simplifying with Trigonometry

[Benhur]

Moved from technical forum, so no template is shown
Summary: I have the expression sin(2x) + sin(2[x + π/3]) and I have to write this in terms of a single function (a single harmonic, rather saying). But I don't know how to do this, and... it seems a little bit weird for me, because I'm merging two sine-wave functions into one. Doesn't the sum of sines result in a more complex body than a simple sine alone?

The exercise that I'm trying to solve says that I must use a trigonometry formula to solve.

 

[DrClaude]

The two sines have the same frequency, so it should indeed be possible to write them as a single sinusoidal function.

I suggest you review the basic trigonometric identities to find the one you need:
https://www2.clarku.edu/faculty/djoyce/trig/identities.html

 

[Benhur]

Thank you, DrClaude. Now I got it.

 

[neilparker62]

Wolfram Alpha sometimes helpful to remind yourself about trig identities: sin(a)+sin(b). (you might have to 'wade' through a lot of extraneous information before you find the required identity)