Question

How do you express `cos(pi/ 4 ) * sin( ( 5 pi) / 8 )` without using products of trigonometric functions?

Answer 1

`- (sqrt2/2)cos (pi.8)`

Explanation:

Use trig table and trig unit circle.
`P = cos (pi/4).sin ((5pi)/8)`
Trig table ---> `cos (pi/4) = sqrt2/2`
`sin ((5pi)/8) = sin (pi/8 + sin ((4pi)/8)) = sin (pi/8 + pi/2) = - cos (pi/8)`
Therefor, P can be expressed as;
`P = - (sqrt2/2)cos (pi/8)`

Note. We can find P by evaluating `cos (pi/8)`, using the trig identity: `cos 2a = 2cos^2 a - 1`