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

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Answer 1 · 2016-07-04T07:09:33

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

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

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

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

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