Question

How do you express `sin(pi/12) * cos(( 17 pi)/12 )` without products of trigonometric functions?

Answer 1

`P = - sin^2 (pi/12)`

Explanation:

`P = sin (pi/12).cos ((17pi)/12).`
First, find `cos ((17pi)/12)`
`cos ((17pi)/12) = cos ((5pi)/12 + pi) = - cos ((5pi)/12)`(supplementary)
`cos ((5pi)/12) = cos (pi/2 - pi/12) = sin (pi/12)`. (complementary arcs)
The product reduces to
`P = - sin^2 (pi/12)`