Question #c5acc

1 Answer
Nghi N
May 26, 2017

#sqrt(2 - sqrt3)/2#

Explanation:

#cos ((3pi)/4 - pi/3) = cos ((9pi - 4pi)/12) = cos ((5pi)/12)#
Find #cos ((5pi)/12)# by using trig identity:
#2cos^2 a = 1 + cos 2a#
In this case, trig table gives:
#cos 2a = cos ((10pi)/12) = cos (5pi/6) = - sqrt3/2#
Call #cos ((5pi)/12) = cos t#, we get:
#2cos^2 t = 1 - sqrt3/2 = (2 - sqrt3)/2#
#cos^2 t = (2 - sqrt3)/4#
#cos t = +- sqrt(2 - sqrt3)/2#
Since #(5pi)/12# is in Quadrant 1, its cos is positive -->
#cos ((5pi)/12) = cos t = sqrt(2 - sqrt3)/2#

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