Trigonometry Equations?

Question

How do you find the value of x with restriction 0<x<360? 

Equation is 
cos^2x = 2 - cosx

Answer 1

The trigonometric equation is cos²x = 2 - cosx

cos² x + cosx - 2 = 0

cos² x + 2cosx - cosx - 2 = 0

cosx(cosx + 2) - 1(cosx + 2) = 0

(cosx + 2)(cosx - 1) = 0

cosx + 2 = 0 and cosx = 1

cosx = - 2 and cosx = 1

cosx = - 2 is does not exist.

Now solve cosx = 1

The general solution of cos(x) = cos(α) is x = 360n ± α, where n is an integer.

cosx = 1

cosx = cos(0)

For n = 0, x = 360(0) ± 0 = 0

For n = 1, x = 360(1) ± 0  = 360

There are no solutions in the interval  0 < x < 360.

The solutions in the interval 0⁰ ≤ x ≤ 360⁰ are 0⁰, 360⁰.