How do you express sin(pi/12) * cos(pi/4 ) without products of trigonometric functions?

1 Answer
Nghi N.
Jun 19, 2016

(sqrt2/4)sqrt(2 - sqrt3)

Explanation:

P = sin (pi/12).cos (pi/4)
Trig table --> cos (pi/4) = sqrt2/2.
Then P can be expressed as: P = (sqrt2/2)sin (pi/12)
We can evaluate sin (pi/12), using the trig identity:
cos 2a = 1 - 2sin^2 a
cos (pi/6) = sqrt3/2 = 1 - 2sin^2 (pi/12)
2sin^2 (pi/12) = 1 - sqrt3/2 = (2 - sqrt3)/2
sin^2 (pi/12) = (2 - sqrt3)/4
sin (pi/12) = +- sqrt(2 - sqrt3)/2
Take the positive value because sin pi/12 is positive
Finally,
P = (sqrt2/4).sqrt(2 - sqrt3)

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