If cos^4(3x)-sin^4(3x)=cos(g(x)) then

Question

g(x)=?

Use a^4-b^4=(a^2-b^2)(a^2+b^2)!

thanks in advance for any help!

Answer 1

cos^4(3x)-sin^4(3x)
= (cos^2 (3x) + sin^2 (3x)(cos^2 (3x ) - sin^2 (3x))
= (1)(cos (6x)

= cos 6x)

Besides using the difference of squares in the second line, I used:
sin^2 Ø + cos^2 Ø = 1 , and
cos 2Ø = cos^2 Ø - sin^2 Ø

Answer 2

Now I see how it works. Thanks for the help!