Give the exact value of cos5pi8sin5pi8 I thought I was suppo

Give the exact value of cos(5pi/8)sin(5pi/8) I thought I was suppose to use the product formula sinxcosy=1/2[sin(x+y)+sin(x-y)] but not sure how to proceed

Solution

We have given cos(5pi/8)sin(5pi/8)

we use sinxcosy=1/2[sin(x+y)+sin(x-y)] since sin(x+y)=sinxcosy+cosxsiny

we have given x=5pi/8,y=5pi/8

we can write cos(5pi/8)sin(5pi/8)=1/2 *(sin(5pi/8 +5pi/8)+sin(5pi/8 -5pi/8))

=1/2 *(sin(10pi/8)+sin(0))

=1/2 *(sin(5pi/4)+sin(0))

=sin(5pi/4)/4

=(-1/sqrt(2))/4

=-1/(4*sqrt(2))

cos(5pi/8)sin(5pi/8)=-1/(4*sqrt(2))