Question

Over the interval [0,2pi), what are the solutions to cos(2x) = cos(x)? check all that apply​

Answer 1

$\cos(2x) = \cos(x)$

Solution (1)

$2x = x + 2k\pi$

$2x - x = 2k\pi$

$x = 2k\pi$

for k=0 / for k=1 / for k=-1

x=0 / x=2π / x=-2π

acc / acc / rej

solution (2)

$2x = - x + 2k\pi$

$2x + x = 2k\pi$

$3x = 2k\pi$

$x = \frac{2k\pi}{3}$

for k=0 / for k=1 / for k=-1

x=0 / x=2π/3 / x=-2π/3

acc / acc / rej

Note that i'm trying values of K which make the answer belong to our interval;

So our solution which i will represent as a set is;

S € {0,2π/3,2π}