How do you solve #cos2x-cosx=0# using the double angle identity?

1 Answer
Nghi N.
Oct 23, 2015

Solve cos 2x - cos x = 0

Ans: #0; 2pi; +- (2pi)/3#

Explanation:

Replace in the equation (cos 2x) by #(2cos^2 x - 1)#, then solve the quadratic equation in cos x:
#2cos^2 x - cos x - 1 = 0#.

Since (a + b + c = 0), use the Shortcut. The 2 real roots are:
cos x = 1 and #cos x = c/a = -1/2.#
a. cos x = 1 --> x = 0 and #cos x = 2pi.#
b. #cos x = -1/2# --> #x = +- (2pi)/3#

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