Question

How do you express `sin(pi/ 4 ) * sin( ( pi) / 6 )` without using products of trigonometric functions?

Answer 1

`sin(pi/2)*sin(pi/6) = sqrt(2)/4`

Explanation:

`pi/4` and `pi/6` are common angles
with
`color(white)("XXX")sin(pi/4)=1/sqrt(2)`
and
`color(white)("XXX")sin(pi/6)=1/2`

So
`color(white)("XXX")sin(pi/4)*sin(pi/6)= 1/sqrt(2)*1/2=1/(2sqrt(2))= sqrt(2)/4`