How do you use the half angle identity to find exact value of Cos(-5pi/12)?

1 Answer
Aug 10, 2015

Find #cos ((-5pi)/12)#

Ans: #+ sqrt(sqrt3 - 2)/2#

Explanation:

Call #cos ((-5pi)/12) = cos t#
#cos 2t = cos ((-10pi)/12) = cos ((5pi)/6) = -cos (pi/6) = -sqrt3/2#
Use trig identity: #cos 2t = 2cos^2 t - 1#

#cos 2t = sqrt3/2 = 2cos^2t - 1.#
#2cos^2 t = sqrt3/2 - 1 = (sqrt3 - 2)/2#
#cos^2t = (sqrt3 -2)/4 #

#cos t = cos ((-5pi)/12) = +-sqrt(sqrt3 - 2)/2#
Since #(-5pi)/4# is in quadrant I, then only the positive answer is accepted --># sqrt(sqrt3 - 2)/2#