Question

How do you express `cos(pi/ 4 ) * sin( ( 13 pi) / 8 )` without using products of trigonometric functions?

Answer 1

`(sin((15pi)/16)+sin((11pi)/16))/2`

Explanation:

Use `sin (A+B)cos(A-B)=(sin 2A + sin 2B)/2 =`
Here, `A+B=13pi/8 and A-B=pi/4`
Add and subtract.
`2A = 15pi/8. A + 15pi/16. 2B = 11pi/8. B = 11pi/16`.
Answer: `(sin((15pi)/16)+sin((11pi)/16))/2`