(cos3x)^2+(sin3x)^2=cos(f(x))
find f(x)
cos anything^2 + sin same thing^2 = 1
so cos (f(x)) = 1
f(x) = 0 or 360 or 720 .........
Hey, Steve already answered that for you.
To find the value of f(x), we need to simplify the given equation and identify a trigonometric identity that matches the form of the equation.
Step 1: Simplify the equation:
Using the Pythagorean identity, cos^2θ + sin^2θ = 1, we can simplify the equation as:
(cos^3x)^2 + (sin^3x)^2 = cos(f(x))
(cos^2x)^3 + (sin^2x)^3 = cos(f(x))
(cos^2x + sin^2x)((cos^2x)^2 - cos^2x * sin^2x + (sin^2x)^2) = cos(f(x))
(1)((cos^2x)^2 - cos^2x * sin^2x + (sin^2x)^2) = cos(f(x))
(cos^4x - cos^2x * sin^2x + sin^4x) = cos(f(x))
Step 2: Identify a trigonometric identity:
In this step, we need to identify a trigonometric identity that matches the form of the simplified equation. After observing the equation, we can see that it matches the form of the double-angle identity:
cos(2θ) = cos^2(θ) - sin^2(θ)
Step 3: Apply the trigonometric identity:
By comparing the double-angle identity with the simplified equation, we can equate the terms:
cos(f(x)) = cos(2x)
Therefore, f(x) = 2x.
Therefore, the value of f(x) is 2x.