To solve the equation 2cos(x)^2 - 1 = 0, we first need to isolate the cosine term.
Adding 1 to both sides of the equation, we get:
2cos(x)^2 = 1
Next, divide by 2 to solve for cos(x)^2:
cos(x)^2 = 1/2
Taking the square root of both sides, we get:
cos(x) = ±√(1/2)
Since cosine is positive in the first and fourth quadrants, the solutions for x will be:
x = ±π/4 + 2nπ , where n is an integer.
Therefore, the complete solution to the equation 2cos(x)^2 - 1 = 0 is:
x = ±π/4 + 2nπ, where n is an integer.
To solve the equation 2cos(x)^2 - 1 = 0, we first need to isolate the cosine term.
Adding 1 to both sides of the equation, we get:
2cos(x)^2 = 1
Next, divide by 2 to solve for cos(x)^2:
cos(x)^2 = 1/2
Taking the square root of both sides, we get:
cos(x) = ±√(1/2)
Since cosine is positive in the first and fourth quadrants, the solutions for x will be:
x = ±π/4 + 2nπ , where n is an integer.
Therefore, the complete solution to the equation 2cos(x)^2 - 1 = 0 is:
x = ±π/4 + 2nπ, where n is an integer.