How do you express cos(pi/ 3 ) * sin( ( 15 pi) / 8 ) without using products of trigonometric functions?

1 Answer
Nghi N.
Feb 25, 2016

P = 1/2 - (sqrt(2 + sqrt2)/2)

Explanation:

P = cos (pi/3).sin ((15pi)/8)
cos (pi/3) = 1/2
sin ((15pi)/8) = sin (2pi - pi/8) = - sin pi/8.
Find sin (pi/8) by using trig identity:
cos (pi/4) = 2cos^2 (pi/8) - 1 = sqrt2/2
2cos^2 (pi/8) = 1 + sqrt2/2 = (2 + sqrt2)/2
cos^2 (pi/8)^2 = (2 + sqrt2)/4
cos (pi/8) = (sqrt(2 + sqrt2))/2 (cos (pi/8) is positive.)
P = 1/2 - (sqrt(2 + sqrt2))/2

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