How do you solve #cos 2x = - sqrt3 / 2# using the double angle identity?

1 Answer
Nghi N.
Oct 13, 2015

Solve: #cos 2x = -sqrt3/2#

Ans: #+- 75^@ and +- 105^@#

Explanation:

Solving by double angle identity: #cos 2a = 2cos^2 a - 1#
#2cos^2 x - 1 = - sqrt3/2#
#2cos^2 x = 1 - sqrt3/2 = (2 - sqrt3)/2#
#cos^2 x = (2 - sqrt3)/4#
cos x = +- sqrt(2 - sqrt3)/2 = +-0.517/2 = +- 0.258

a. cos x = 0.258 --> #x = +- 75^@#
b. cos x = - 0.258 --> #x = +- 105^@#
Check by calculator :
#x = +- 75# --> #2x = +- 150# --> cos 2x = - 0.87 = -sqrt3/2. OK
#x = +- 105# --> #2x = +-210# --> cos 2x = - 0.87. OK

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