How do you express cos( (5 pi)/6 ) * cos (( 5 pi) /12 ) without using products of trigonometric functions?

1 Answer
Nghi N.
Mar 18, 2016

P = - (sqrt3/4)(sqrt(2 - sqrt3))

Explanation:

P = cos ((5pi)/6).cos ((5pi)/12)
Trig table --> cos ((5pi)/6) = -sqrt3/2
Find cos ((5pi)/12) by the identity: cos 2a = 2cos^2a - 1
cos ((5pi)/6) = -sqrt3/2 = 2cos^2 ((5pi)/12) - 1
2cos^2 ((5pi)/12) = 1 - sqrt3/2 = (2 - sqrt3)/2
cos^2 ((5pi)/12) = (2 - sqrt3)/4
cos ((5pi)/12) = sqrt(2 - sqrt3)/2 -->cos ((5pi)/12) is positive.
Finally,
P = (-sqrt3/2)(sqrt(2 - sqrt3)/2) = - (sqrt3/4)(sqrt(2 - sqrt3))

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