How do you express cos(π4)sin(π8) without using products of trigonometric functions?

1 Answer
Jul 4, 2016

cos(π4)sin(π8)=12sin(3π8)12sin(π8)

Explanation:

As sin(A+B)=sinAcosB+cosAsinB and

sin(AB)=sinAcosBcosAsinB

and subtracting second equation from first equation we get

sin(A+B)sin(AB)=2cosAsinB or

cosAsinB=sin(A+B)2sin(AB)2

Hence cos(π4)sin(π8)

= sin(π4+π8)2sin(π4π8)2

= 12sin(3π8)12sin(π8)