Question

How do you use the sum and difference identity to evaluate `sin(pi/12)`?

Answer 1

`(sqrt2/4)(1 - sqrt3)`

Explanation:

Use trig identity:
sin (a - b) = sin a.cos b - sin b.cos a
`sin (pi/12) = sin (pi/3 - pi/4) = sin (pi/3).cos (pi/4) - sin (pi/4).(cos pi/3)`
Trig table gives;
`sin (pi/3) = 1/2`, and `cos (pi/3) = sqrt3/2`
`sin (pi/4) = sqrt2/2`, and `cos (pi/4) = sqrt2/2`
We get:
`sin (pi/12) = (1/2)(sqrt2/2) - (sqrt2/2)(sqrt3/2)`
`= (sqrt2/4)(1 - sqrt3)`