Answer:
A
Step-by-step explanation:
We want to solve the equation:
For the interval [0, 2π).
First, we can move all the terms to one side. Start off by subtracting sin(x) from both sides:
We can factor:
By the Zero Product Property:
Solve for each case:
Use the unit circle to solve:
Hence, our answer is A.
*Please note that we should not simply divide both sides by sin(x) to acquire 2sin(x) = 1. The problem with the operation is that we are dividing by sin(x), yet we do not know what the value of x is. Thus, one or more values of x may result in sin(x) = 0, and we cannot divide by 0. Hence, we are required to subtract and then factor, unless the question specifically states that sin(x) ≠ 0.