Question

How do you express `sin(pi/ 8 ) * cos(( 13 pi)/8 )` without products of trigonometric functions?

Answer 1

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

Explanation:

On the trig unit circle,
`cos ((13pi)/8) = cos ((-3pi)/8 + 2pi) = cos ((-3pi)/8) = cos ((3pi)/8)`
`= cos ((4pi)/8 - pi/8) = cos (pi/2 - pi/8) = sin (pi/8)`
Therefor, the expression can be reduced to -->
`P = sin (pi/8).cos((13pi)/8) = sin^2 (pi/8)`