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) $y = 4 \cos ( 2 \pi x + b t )$

Question

Quizplus · Accepted Answer

The given equation $y = 4 ( \cos 2 \pi x \cos b t + \sin 2 \pi x \sin b t )$ can be rewritten using the trigonometric identity $\cos(A - B) = \cos A \cos B + \sin A \sin B$, which results in $y = 4 \cos ( 2 \pi x - b t )$, making option B correct.

Verify That the Equation Is an Identity y=4(cos⁡2πxcos⁡bt+sin⁡2πxsin⁡bt)y = 4 ( \cos 2 \pi x \cos b t + \sin 2 \pi x \sin b t )y=4(cos2πxcosbt+sin2πxsinbt)

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