Question

How do you express `sin(pi/ 8 ) * cos(( ( 7 pi) / 12 )` without using products of trigonometric functions?

Answer 1

`color(brown)(=> (sin ((17pi)/24) - sin((11pi)/24))/2`

Explanation:

`sin(pi/8) * cos ((7pi)/12)`

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

`=> (1/2)(sin ((pi/8) + ((7pi)/12)) + sin ((pi/8) - ((7pi)/12)))`

`=> (1/2) (sin ((17pi)/24) - sin((11pi)/24))`

`=> (sin ((17pi)/24) - sin((11pi)/24))/2`