How do you express sin(pi/12) * cos(( 19 pi)/12 ) sin(π12)cos(19π12) without products of trigonometric functions?

1 Answer
Mar 25, 2016

sin^2 (pi/12)

Explanation:

The trig unit circle and the property of complementary arcs give -->
cos ((19pi)/12) = cos ((7pi)/12 + pi) = -cos ((7pi)/12) =cos(19π12)=cos(7π12+π)=cos(7π12)=
= - cos (pi/12 + pi/2) = sin (pi/12)=cos(π12+π2)=sin(π12)
Reminder: cos (a + pi/2) = - sin acos(a+π2)=sina

Finally, the product can be expressed as:
P = sin^2 (pi/12)P=sin2(π12)