How do you solve #2cos^2(t)+cos(t)=1#?

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How do you solve #2cos^2(t)+cos(t)=1#?

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Answer 1 · 2015-06-13T05:10:15

Solve; #2cos^2 t + cos t - 1 = 0#

Explanation:

Call cos x = p, and solve the quadratic equation:
#y = v^2 + v - 1 = 0.#
Since a - b + c = 0, use shortcut: one real root is v = -1 and the other #v = -c/a = 1/2.#
Next solve the 2 basic equations: cos x = -1 and #cos x = 1/2#
a. v = cos x = -1 -> #x = pi#
b. #cos x = 1/2 -> x = +- pi/3 #

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How do you solve #2cos^2(t)+cos(t)=1#?

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