Verify That the Equation Is an Identity $y = 4 ( \cos 2 \pi x \cos b t + \sin 2 \pi x \sin b t )$

Multiple Choice

Verify that the equation is an identity.
-A vibrating wire has a vertical displacement given by $y = 4 ( \cos 2 \pi x \cos b t + \sin 2 \pi x \sin b t )$ . Assume $\mathrm { b }$ and $\mathrm { t }$ are constants. Write $\mathrm { y }$ as a cosine function of $\mathrm { x }$ .

A) $y = 8 \cos ( 2 \pi x + b t )$
B) $y = 4 \cos ( 2 \pi x - b t )$
C) $y = \cos ( 2 \pi x - b t )$
D) $y = 4 \cos ( 2 \pi x + b t )$