Rewriting Equation 15: Two Transverse Waves Moving in Opposite Directions

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Homework Statement

Show that the solution to the wave equation, Equation 15, can be rewritten as the sum of two transverse waves moving in opposite directions along the wire.

Equation 15:y(x,t) = A(sin(2*pi*f*x)/v))*cos(2*pi*f*t)

Homework Equations

Superposition: y(x,t) = f(x-ct) + g(x+ct)
Period: T = (1/f) = (2 * pi/omega)
Wavelength = (2* pi)/k

The Attempt at a Solution

I really just don't know where to start. Do I need a trig identity? I am completely not sure how to separate it into two terms that use like superposition for example. This equation shown above is not the standard wave equation but with variables substituted inside. I am trying to solve this or show for the topic of standing waves on a wire.

 

[fzero]

You need to invert the trig identities for \sin(A\pm B) to derive a formula for the product \sin A \cos B.

 

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So, what do you mean by inverting the trig identity?

Could you possibly, show me how to start this question?

sin Alpha cos β = ½[sin (Alpha + β) + sin (Alpha − β)] <--- This is a trig identity I should be using?

So would i just set Alpha = 2*pi*f*x/v and beta = 2*pi*f*t?