Question

Which expression is equivalent to cos(4x) + cos(2x)?
2cos(3x)cos x
-2sin(3x)sin x
2sin(3x)sin x
-2cos(3x)cos x

Answer 1

Expand cos(4x) + cos(2x)

Answer 2

You can probably use these identities
$$
\cos 4x=\cos (2\times2x)
$$
But also
$$
\cos 2x = \cos^2x - \sin^2x\\
\cos^2x=1-\sin^2x
$$

Answer 3

im lost

Answer 4

is it 2cos(3x)cos x?

Answer 5

this is ridiculous

Answer 6

Refer to the attached Mathematica plots.

Answer 7

one approach
let 2A =B
so you have cos 2B + cos B
cos n theta = 2 cos theta (n-1) cos theta - cos (n-2) theta
here n = 2 and theta = B
what do you get ?
next cos P + cos Q = 2 cos (P + Q )/2 * cos (P - Q)/2
substitute and simplify