How do you express sin(pi/ 4 ) * sin( ( 13 pi) / 12 ) without using products of trigonometric functions?

1 Answer
Nghi N.
Feb 29, 2016

P = -(sqrt2/4)(sqrt(2 - sqrt3))

Explanation:

Product P = sin (pi/4).sin ((13pi)/12)
Trig table --> sin pi/4 = sqrt2/2.
sin ((13pi)/12) = sin (pi/12 + pi) = - sin pi/12
Find sin (pi/12) by identity:
cos (pi/6) = 1 - 2sin^2 (pi/12) = sqrt3/2
sin^2 (pi/12) = (2 - sqrt3)/4
sin (pi/12) = sqrt(2 - sqrt3)/2. (sin (pi/12) is positive)
Finally:
P = - (sqrt2/4)(sqrt(2 - sqrt3))

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