Answer: 0
Step-by-step explanation: To solve the equation cos(x)(cos(x) - 1) = 0, we can use the zero product property, which states that if a product of factors equals zero, then at least one of the factors must equal zero.
Here are the steps to solve the equation:
1. Set each factor equal to zero and solve for x:
a) cos(x) = 0: This occurs when x is equal to (2n + 1)π/2, where n is an integer. In this case, the smaller value for n = 0 would be x = π/2, and the larger value for n = 0 would be x = (2(0) + 1)π/2 = π/2 as well.
b) cos(x) - 1 = 0: Add 1 to both sides of the equation to isolate the cosine term.
cos(x) = 1: This occurs when x is equal to 2nπ, where n is an integer. In this case, the smaller value for n = 0 would be x = 2(0)π = 0, and the larger value for n = 0 would be x = 0 as well.
2. Therefore, the solutions for x are x = π/2 and x = 0.
Note: Since cos(x) can only take on values between -1 and 1, these are the only solutions that satisfy the equation cos(x)(cos(x) - 1) = 0.