A Transverse Periodic Wave Is Represented by the Equation Y(x,t) $\omega$

A transverse periodic wave is represented by the equation y(x,t) = A1 sin( $\omega$ t - kx) .Another transverse wave is represented by the equation y(x,t) = A2 sin( $\omega$ t + kx) .What is the equation that represents the superposition of the two waves?

A) y(x,t) = (A1+A2) sin( $\omega$ t) cos(kx) + (+A1+A2) cos( $\omega$ t) sin(kx)
B) y(x,t) = (A1+A2) sin( $\omega$ t) cos(kx) + (-A1-A2) cos( $\omega$ t) sin(kx)
C) y(x,t) = (A1-A2) sin( $\omega$ t) cos(kx) + (-A1+A2) cos( $\omega$ t) sin(kx)
D) y(x,t) = (A1+A2) sin( $\omega$ t) cos(kx) + (-A1+A2) cos( $\omega$ t) sin(kx)

Correct Answer:

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