Posted by **Kindell** on Monday, March 17, 2008 at 2:15am.

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?

- Pre Cal -
**drwls**, Monday, March 17, 2008 at 6:25am
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

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