How do you express sin(pi/12) * cos(( 13 pi)/8 ) sin(π12)cos(13π8) without products of trigonometric functions?

1 Answer
Mar 31, 2016

sin (pi/8).sin (pi/12)

Explanation:

P = sin (pi/8).cos ((13pi)/8)P=sin(π8).cos(13π8)
Trig unit circle, properties of supplementary and complementary arcs give -->
cos ((13pi)/8) = cos ((5pi)/8 + pi)) = - cos ((5pi)/8) = cos(13π8)=cos(5π8+π))=cos(5π8)=
= - cos (pi/8 + pi/2) = sin (pi/8).=cos(π8+π2)=sin(π8).
Therefor,
P = sin (pi/12).sin (pi/8)P=sin(π12).sin(π8)