Question

How do you express `sin(pi/12) * cos(pi/6 )` without products of trigonometric functions?

Answer 1

`= (sqrt3/4)(sqrt(2 - sqrt3))`

Explanation:

Product `P = sin (pi/12).cos (pi/6)`
Trig table --> `cos (pi/6) = sqrt3/2`
Find sin (pi/12) by using trig identity:
`1 - cos (pi/6) = 2sin^2 (pi/12)`
`2sin^2 (pi/12) = 1 - sqrt3/2 = (2 - sqrt3)/2`
`sin^2 (pi/12) = (2 - sqrt3)/4`
`sin (pi/12) = sqrt(2 - sqrt3)/2` - (sin (pi/12) is positive)
Finally:
`P = (sqrt3/4)(sqrt(2 - sqrt3))`