How do you find the exact values of cos 15 using the half angle formula?

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Answer 1 · 2015-08-30T18:36:37

#color(red)(cos15 = sqrt(2 +sqrt3)/2)#

The cosine half-angle formula is

#cos(x/2) = ±sqrt((1 + cos x) / 2)#

The sign is positive if #x/2# is in the first or fourth quadrant and negative if #x/2# is in the second or third quadrant.

#15°# is in the first quadrant, so the sign is positive.

#15= 30/2#

∴ #cos15 = cos(30/2) = sqrt((1+cos30)/2)#

#cos15 = sqrt((1 + sqrt3/2)/2) = sqrt((2 + sqrt3)/4)#

#cos15 = sqrt(2 +sqrt3)/2#