Question

Question #e8695

Answer 1

`x in {pi/6+pin, (5pi)/6+pin}, n in ZZ`

Explanation:

Using a unit circle or knowledge of common angles, we can find that `cos(theta) = 1/2` when `theta = pi/3+2pin` or `theta = (5pi)/3+2pin` where `n in ZZ`.

Applying that to the given equation:

`cos(2x) = 1/2`

`=> 2x = pi/3+2pin` or `2x = (5pi)/3+2pin, n in ZZ`

`:. x = pi/6+pin` or `x = (5pi)/6+pin, n in ZZ`