Question

2cos*2x-cosx=1 find all solutions to the equation on the domain [0,2ð]

i got ð/4, 7ð/4, 3ð/4, and 5ð/4 but only got two out of four points... what did i do wrong?

Answer 1

Is cos*2x supposed to mean cos^2 x?
Is 2ð supposed to mean 2 pi?
If so,
2 cos^2x - cos x -1 = 0
which factors into
(2 cos x +1)(cos x -1) = 0
The solutions occur where cos x = -1/2 or +1

If cos*2x means cos(2x), then
2[2 cos^2 x -1) - cos x -1 = 0
4 cos^2 x -cos x -3 = 0
(4 cosx +3)(cosx - 1) = 0
x is where cos x = -3/4 or +1