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

1 Answer
Nghi N.
Feb 26, 2016

(2 - sqrt3)/4

Explanation:

On the unit circle, using property of complementary arcs:
cos ((5pi)/12) = sin (pi/2 + (5pi)/12) = sin ((11pi)/12) = sin pi/12
Product P = sin (pi/12).cos ((5pi)/12) = sin^2 (pi/12).
Find sin^2 (pi/12).
Use trig identity: cos (pi/6) = 1 - 2sin^2 (pi/12) = sqrt3/2
2sin^2 (pi/12) = 1 - sqrt3/2 = (2 - sqrt3)/2
P = sin^2 (pi/12) = (2 - sqrt3)/4

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