Question

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

Answer 1

`(sqrt2*sqrt(2-sqrt2))/4`

Explanation:

Use the identity: `sin(pi/4)=(sqrt2)/2`

`sin(pi/8)=sqrt((2-sqrt2)/4)`

Hence,

`sin(pi/4)*sin(pi/8)=(sqrt2)/2*sqrt((2-sqrt2)/4)`
`color(white)(xxxxxxxxxxx.)=(sqrt2*sqrt(2-sqrt2))/4`