Question

How do you express `sin(pi/12) * cos(( 19 pi)/12 )` without products of trigonometric functions?

Answer 1

sin^2 (pi/12)

Explanation:

The trig unit circle and the property of complementary arcs give -->
`cos ((19pi)/12) = cos ((7pi)/12 + pi) = -cos ((7pi)/12) =`
`= - cos (pi/12 + pi/2) = sin (pi/12)`
Reminder: `cos (a + pi/2) = - sin a`

Finally, the product can be expressed as:
`P = sin^2 (pi/12)`