Final answer:
To solve the equation 4cos²x - 3 = 0, isolate cos²x, divide by 4, take the square root, and consider the periodicity of the cosine function. The values 4cos²x - 3 = 0 are x = 5π/6 and x = 7π/6.
Step-by-step explanation:
To solve the equation 4cos²x - 3 = 0, we can start by isolating cos²x by adding 3 to both sides of the equation. This gives us 4cos²x = 3. Then, divide both sides by 4 to get cos²x = 3/4.
Taking the square root of both sides, we have cosx = ±√(3/4).
Since the cosine function has a period of 2π, we can find the solutions to the equation within one period. The values of x that satisfy cosx = √(3/4) are x = π/6 and x = 11π/6.
The values of x that satisfy cosx = -√(3/4) are x = 5π/6 and x = 7π/6.