Use the formula for lowering the powers to simplify the expression:
(a) If cos^2 3 x - sin^2 3 x = cos (f(x)), then
f(x) = ;
(b) If cos^4 3 x - sin^4 3 x = cos (g(x)), then
g(x) = .
For part (b), use a^4-b^4=(a^2-b^2)(a^2+b^2)!

Question

Use the formula for lowering the powers to simplify the expression: 
(a) If cos^2 3 x - sin^2 3 x = cos (f(x)), then 
f(x) = ; 
(b) If cos^4 3 x - sin^4 3 x = cos (g(x)), then 
g(x) = . 
For part (b), use a^4-b^4=(a^2-b^2)(a^2+b^2)!

zepdrix · Answer

For part A, we'll want to recall the `Double Angle Identity for Cosine`.
It shows up in several different forms.
But here is the one we're interested in.

$$\large \cos^2\theta-\sin^2\theta=\cos(2\theta)$$

Hmm how can we maybe use this to solve part A?

anonymous · Answer

I found part a but now I just cant get part B