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}(A+B)/(2)\cos (A-B)/(2)`

Here A=4x and B=2x

So

`\begin{gathered} \cos 4x+\cos 2x=2\cos (4x+2x)/(2)\cos (4x-2x)/(2) \\ =2\cos (6x)/(2)\cos (2x)/(2) \\ =2\cos 3x\text{ cosx} \end{gathered}`

So the correct option is 2cos3x cosx