Final answer:
To solve the equation cos(6x) = sin(3x-9), first convert the trigonometric functions into their equivalent forms. Then, set the angles of cos(6x) and cos(π/2 - (3x - 9)) equal to each other and solve for x.
Step-by-step explanation:
To solve the equation cos(6x) = sin(3x-9), we need to find the values of x that satisfy the equation. We can start by converting trigonometric functions into their equivalent forms.
Using the identity sin(θ) = cos(π/2 - θ), we can rewrite the equation as:
cos(6x) = cos(π/2 - (3x - 9))
Since the cosine function is equal only when their angles are equal or differ by a multiple of 2π, we set the angles of cos(6x) and cos(π/2 - (3x - 9)) equal to each other:
6x = π/2 - (3x - 9)
Simplifying the equation:
6x = π/2 - 3x + 9
9x = π/2 + 9
x = (π/2 + 9)/9
Therefore, the value of x that solves the equation is (π/2 + 9)/9.