Question

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

Answer 1

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

Explanation:

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