need help with trig

Question

Use a half angle formula or formula for reducing powers to fill in the blanks in the identity below: = __ + __  cos(__x)

Answer 1

cos2x = 2(cosx)^2 -1 is the general formula for double angles.

2(cosx)^2 = 1 + cos 2x replace x by 2x, and divide by 2 on both sides

(cos2x)^2 = 1/2 + (1/2)cos4x

Answer 2

Hi Chlo. If by (cos(2x))2 you mean cos(2x) raised to the second power, then you have cos^2(2x) and thus you can use the following identity: cos^2(u) = (1 + cos(2u))/2 = 1/2 + 1/2*cos(2u). Now substitute u = 2x into the identity and get: cos^2(2x) = 1/2 + 1/2*cos(2(2x))

Thus cos^2(2x) = 1/2 + 1/2*cos(4x).

Robert

Answer 3

Hi Chlo A.,

Let θ = 2x and use the half-angle identity cos²(θ) = [1 + cos(2θ)]/2:

cos²(2x) = cos²(θ) = [1 + cos(2θ)]/2,

We can write this as:

1/2 + 1/2*cos(2θ), the substitute 2x = θ back in:

1/2 + 1/2*cos(4x), the answers are underlined.

I hope this helps, Joe.