Write the product as a sum or difference Write the product a

Write the product as a sum or difference.

Write the product as a sum or difference. sin x/7 cos 8x/7

sin(x/7)cos(8x/7)

sinA - sinB=2cos(A+B)/2 sin(A-B)/2

1/2(sinA -sinB)= sin(A-B)/2 cos (A+B)/2

comparing the given expression with the above formula we get

A-B/2=x/7 and A+B/2=8x/7

A-B=2x/7 and A+B= 16x/7

A=9x/7 and B = x

Therefore the required expression is

sin(9x/7)/2 -sinx/2