If #2sin^2x - cosx =1# how do you solve for x?

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If #2sin^2x - cosx =1# how do you solve for x?

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Answer 1 · 2015-12-06T05:39:07

Solve #2sin^2 x - cos x = 1#

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

Explanation:

Replace in the equation #sin^2 x# by #( 1- cos^2 x)#:
#2(1 - cos^2 x) - cos x - 1 = 0#
#2 - 2cos^2 x - cos x -1 = 0.#
Solve the quadratic equation in cos x.
#-2cos^2 x - cos x + 1 = 0.#
Since (a - b + c = 0), use shortcut -->
--> cos x = 1 and #cos x = c/a = -1/2#
a. cos x = 1 --> arc x = 0 and #x = 2pi#
b. #cos x = -1/2# --> arc #x = +- (2pi)/3#

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If #2sin^2x - cosx =1# how do you solve for x?

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