SOLUTION: Find all solutions of each equation in the interval [0,2π) 2sin^(2)x-cos(x) =1

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions of each equation in the interval [0,2π) 2sin^(2)x-cos(x) =1      Log On


   

Question 1155028: Find all solutions of each equation in the interval [0,2π)
2sin^(2)x-cos(x) =1
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
2sin%5E2%28x%29-cos%28x%29+=1

2sin%5E2%28x%29-cos%28x%29-1=0

2%281%5E%22%22-cos%5E2%28x%29%29-cos%28x%29-1=0

2-2cos%5E2%28x%29-cos%28x%29-1=0

-2cos%5E2%28x%29-cos%28x%29%2B1=0

Multiply through by -1

2cos%5E2%28x%29%2Bcos%28x%29-1=0

Factor the left side:

matrix%281%2C3%2C%28cos%28x%29%2B1%29%282cos%28x%29-1%29%2C%22%22=%22%22%2C0%29

Use the zero factor principle:



Edwin