Question

How do you express `sin(pi/12) * cos(( 11 pi)/12 )` without products of trigonometric functions?

Answer 1

`- 1/4`

Explanation:

`P = sin (pi/12).cos ((11pi)/12)`
Trig unit circle and property of supplementary arcs -->
`cos ((11pi)/12) = cos (-pi/12 + (12pi)/12) = cos (-pi/12 + pi) =`
`= - cos (pi/12)`
Apply the trig identity: sin 2a = 2sin a.cos a -->
`P = - sin(pi/12).cos (pi/12) = (-1/2)sin (pi/6) = (-1/2)(1/2) = - 1/4`