Use a double or half angle formula to determine value of cos(13π/12)?

1 Answer
Nghi N
May 5, 2018

#- (2 + sqrt3)/2#

Explanation:

#cos ((13pi)/12) = cos (pi/12 + pi) = - cos (pi/12)#
Find #cos ((pi)/12)# by using trig identity:
#2cos^2 a = 1 + cos 2a#.
In this case:
#2cos^2 (pi/12) = 1 + cos (pi/6) = 1 + sqrt3/2 = (2 + sqrt3)/2#
#cos^2 (pi/12) = (2 + sqrt3)/4#
#cos (pi/12) = (2 + sqrt3)/2# --> (#cos (pi/12)# is positive).
Finally,
#cos ((13pi)/12) = - cos (pi/12) = - (2 + sqrt3)/2#

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