How many solutions does the equation cos(x) + cos(−x) = 0 have if 0 < x < 2pi?

Question

(Radian measure is assumed for x.)
(A) infinitely many (B) 1 (C) 2 (D) 3 (E) None of the above.

Answer 1

Since cos(-x) = cos(x) for all x
cosx + cos(-x) = 0
2cosx = 0
cosx = 0
x = π/2 or x = 3π/2 (90° and 270°)