Final answer:
To solve the equation 2sinx² = 1 - cos(x), rearrange it as a quadratic equation 2cos²(x) - cos(x) - 1 = 0. Find the value(s) of cos(x) using factoring, completing the square, or the quadratic formula. Use inverse trigonometric functions to find the corresponding values of x.
Step-by-step explanation:
To solve the equation 2sinx² = 1 - cos(x), we can rearrange it as 2sinx² + cos(x) - 1 = 0.
Now, let's convert sinx² into 1 - cos²(x) using the Pythagorean identity sin²(x) + cos²(x) = 1.
Substituting this in, we get 2(1 - cos²(x)) + cos(x) - 1 = 0.
Simplifying, we have 2cos²(x) - cos(x) - 1 = 0.
This is a quadratic equation in terms of cos(x), which can be solved using factoring, completing the square, or the quadratic formula. Once we find the value(s) of cos(x), we can use inverse trigonometric functions to find the corresponding values of x.