Question

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

Answer 1

`-(sqrt2/2)sin (pi/8)`

Explanation:

`P = sin (pi/8).cos ((3pi)/4)`
Trig table -->
`cos ((3pi)/4) = -sqrt2/2`
Then, P can be expressed as:
`P = -(sqrt2/2)sin (pi/8)`
We can evaluate P by finding sin (pi/8). applying the trig identity:
`cos (pi/4) = sqrt2/2 = 1 - 2sin^2 (pi/8)`