How do you use the double angle or half angle formulas to solve #2 + 3cos2x = cosx#?

1 Answer
Nghi N.
Oct 17, 2015

Solve #2 + 3cos 2x = cos x#

Ans: #+- 60^@ and +-109^@47#

Explanation:

Replace in the equation (cos 2x) by #(2cos^2 x - 1)# -->
#2 + 3(2cos^2 x - 1) = cos x#
#6cos^2 x - cos x - 1 = 0#.
Solve this quadratic equation in cos x.
#D = d^2 = b^2 - 4ac = 1 + 24 = 25# --> #d = +- 5#
#cos x = 1/12 +- 5/12# --> #cos x = 1/2# and #cos x = -1/3#

a. #cos x = 1/2# --> #x = +- 60^@#
b. #cos x = -1/3# --> #x = +- 109.47#

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