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

1 Answer
Jul 4, 2016

cos(pi/4)sin(pi/8)=1/2sin((3pi)/8)-1/2sin(pi/8)

Explanation:

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

sin(A-B)=sinAcosB-cosAsinB

and subtracting second equation from first equation we get

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

cosAsinB=sin(A+B)/2-sin(A-B)/2

Hence cos(pi/4)sin(pi/8)

= sin(pi/4+pi/8)/2-sin(pi/4-pi/8)/2

= 1/2sin((3pi)/8)-1/2sin(pi/8)