Question

How do you express `sin(pi/ 8 ) * cos(( ( pi) / 3 )` without using products of trigonometric functions?

Answer 1

`(sin((11pi)/24)-sin((5pi)/24))/2`

Explanation:

Use
`sin 2A - sin 2B = 2 cos(A+B)sin(A-B)`.

Here, `A+B=pi/3 and A-B=pi/8`.

So, `2A=11pi/24 and 2B=5pi/24`.

Answer: `(sin((11pi)/24)-sin((5pi)/24))/2`