Question

How do you express `sin(pi/12) * cos(pi/8 )` without products of trigonometric functions?

Answer 1

`(1/2)[sin (pi/24) + (1/2)sin ((5pi)/24)]`

Explanation:

`P = sin (pi/12).cos (pi/8)`
Use trig identity:
`sin a.cos b = (1/2)[sin (a - b) + (1/2)(sin (a + b)]`
We have:
`sin (a - b) = sin ((pi/8) - (pi/12)) = sin (pi/24)`
`sin (a + b) = sin ((pi/8) + (pi/12)) = sin ((5pi)/24)`
There for, P can be expressed as:
`P = (1/2)[sin (pi/24) + (1/2)sin ((5pi)/24)]`