Are c1 cos(wt) + c2 sin(wt) and A sin(wt + phi) Equivalent?

[Knight]

Hi. I have to show that
x(t)=c1 cos(wt) + c2 sin(wt) '(1)'
and
x(t) = A sin(wt + phi)
are equivalent. I know I have to use
sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta)
or
cos(alpha +beta)= cos(alpha)cos(beta) - sin(alpha)sin(beta)

I have been strugling with this problem for a long time, trying to multiply expression (1) with cos(beta) and so on but I don't think I am getting anywere. Could someone please give me a little hint how to begin on this problem?

 

[Astronuc]

Try applying sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) to x(t) = A sin(wt + phi)

Let alpha = wt and beta = phi, and since phi is some constant (phase angle), then sin(phi) and cos(phi) are constants.

 

[Knight]

That was easy.
Thanks.