Question

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

Answer 1

`- sin^2 (pi/8)`

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)`
Therefor, the product can be expressed as:
`P = sin (pi/8).cos ((5pi)/8) = - sin^2 (pi/8)`