Question

How do you express `sin(pi/ 8 ) * cos(( ( 7 pi) / 4 )` without using products of trigonometric functions?

Answer 1

`P = (sqrt2/2)sin (pi/8)`

Explanation:

`P = sin (pi/8)cos ((7pi)/4)`
`cos ((7pi)/4) = cos (-pi/4 + 2pi)= cos (-pi/4) = cos pi/4 = sqrt2/2`
P can be expressed as:
`P = (sqrt2/2)sin (pi/8)`
We can find P by evaluating #sin (pi/8), if being asked.