Question

How do you express `sin(pi/ 4 ) * sin( ( 3 pi) / 8 )` without using products of trigonometric functions?

Answer 1

`color(maroon)(=> (sin ((5pi)/8) - sin (pi/8)) / 2`

Explanation:

https://lo.wikipedia.org/wiki/%E0%BB%84%E0%BA%95%E0%BA%A1%E0%BA%B8%E0%BA%A1

`sin A * sin B = (1/2) * (sin (A+B) + sin (A-B)), Identity`

`sin (pi/4) * sin((3pi)/8)`

`=> (1/2) * (sin (pi/4 + (3pi)/8) + sin (pi/4 - (3pi) / 8)`

`=.> (1/2) (sin ((5pi)/8) + sin -(pi/8))`

`color(maroon)(=> (sin ((5pi)/8) - sin (pi/8)) / 2`