Question

Select the correct answer.Which expression is equivalent to cos(4x) + cos(2x)?O A. 2cos(3.c)cos yOB. -2sin(3x)sinoOC. 2sin(3x)sinsOD. -2cos(35)COSI

Answer 1

We will use the following identity

$\cos A+\cos B=2\text{cos}\frac{A+B}{2}\cos \frac{A-B}{2}$

Here A=4x and B=2x

So

$\begin{gathered} \cos 4x+\cos 2x=2\cos \frac{4x+2x}{2}\cos \frac{4x-2x}{2} \\ =2\cos \frac{6x}{2}\cos \frac{2x}{2} \\ =2\cos 3x\text{ cosx} \end{gathered}$

So the correct option is 2cos3x cosx