Question

How do you express `sin(pi/ 4 ) * sin( ( 1 3 pi) / 8 )` without using products of trigonometric functions?

Answer 1

`P = - (sqrt2/2)sin ((3pi)/8)`

Explanation:

`P = sin (pi/4).sin ((13pi)/8).`
Trig table --> `sin (pi/4) = sqrt2/2`
#sin ((13pi)/8) = sin ((-3pi)/8 + (16pi)/8) = sin (-3pi/8 + 2pi) = = sin ((-3pi)/8) = - sin ((3pi)/8)#
P can be expressed as:
`P = - (sqrt2/2)sin ((3pi)/8)`

Note. We can evaluate P after finding `sin ((3pi)/8)` by the trig identity:
`cos ((3pi)/4) = -sqrt2/2 = 1 - 2sin^2 ((3pi)/8)`