Question

How do you express `cos(pi/ 4 ) * sin( ( 19 pi) / 12 )` without using products of trigonometric functions?

Answer 1

`P = (sqrt2/2)sin (pi/12)`

Explanation:

Trig table --> `cos (pi/4) = sqrt2/2`, then
`P = (sqrt2/2)sin ((19pi)/12).`
Trig unit circle, and property of complementary arcs give: -->
`sin ((19pi)/12) = - sin ((5pi)/12) = - cos (pi/2 - (5pi)/12) =`
`= - cos (pi/12) = cos (pi/12)`

Finally, P can be expressed as:
`P = (sqrt2/2)sin (pi/12)`.
We can find P by evaluating `sin (pi/12)`, if required.