How do you express sin(pi/ 8 ) * cos(( 5 pi)/8 ) sin(π8)cos(5π8) without products of trigonometric functions?

1 Answer
Mar 25, 2016

- sin^2 (pi/8)sin2(π8)

Explanation:

Trig unit circle and the property of complementary arcs give -->
cos ((5pi)/8) = cos (pi/8 + (4pi)/8) = cos (pi/8 + pi/2) = - sin (pi/8)cos(5π8)=cos(π8+4π8)=cos(π8+π2)=sin(π8)
Therefor, the product can be expressed as:
P = sin (pi/8).cos ((5pi)/8) = - sin^2 (pi/8)P=sin(π8).cos(5π8)=sin2(π8)