(cos3x)^4+(sin3x)^4=cos(g(x))
find g(x)
To find g(x), we need to simplify the given expression by using the trigonometric identity:
cos^2(x) + sin^2(x) = 1
We can apply this identity to the given expression:
(cos^3(x))^4 + (sin^3(x))^4 = cos(g(x))
Let's simplify each term:
(cos^3(x))^4 = cos^12(x)
(sin^3(x))^4 = sin^12(x)
Now we can substitute these simplified terms into the equation:
cos^12(x) + sin^12(x) = cos(g(x))
Since cos^2(x) + sin^2(x) = 1, we can rewrite the equation as:
cos^12(x) + (1 - cos^2(x)) = cos(g(x))
Expanding the equation further:
cos^12(x) + 1 - cos^2(x) = cos(g(x))
Rearranging the terms:
cos^12(x) - cos^2(x) + 1 = cos(g(x))
Finally, comparing this equation to the original equation, we can conclude that g(x) = 12x.