Question

Determine the specific solutions (if any) to the equation on the interval [0,2x) 2 cose + cos 0 -1 = 0 What are the solutions to the equation 2 cos?o + cos 0 - 1 = 0 on the interval (0,2x)? Select the correct choice below and fill in any answer boxes within your choice. O A. The solutions are (Simplify your answer. Type an exact answer, using as needed. Use a comma to separate answers as needed.) OB. There are no solutions in the interval [0,2x).

Answer 1

Solution : 2 costo + coso-1=0 Let cos o = x => 2x²+x-1=0 This is a quadratic equation in So, by using quadratic formula we get - - (1) √(0²- 4 (2) (-1) 2 (2) x = - + - + 8 - X = -1 + 3 > X = -4 , 2 , => X = -1, 1 2 So, Cos o = -1 or Coso 2 Cos o = 7T

Now, cos o = 2 Klo also, Cos o = cos (270) cos (27 cos o = - = cos o = cos (5) 5T Hence, T, 5T I w/