If m andare the roots of a.cosx+b.sinx=c. Then find value of sin(m).sin(n)

since m and n are the roots so we can write,
a cosm + b sinm = c and a cosn + b sin n = c ,

From here find the values of sin m and sin n in terms of a,b,c, and cosm/cosn and multiply the factors.

Now as per the desired result you can simplify.

Thanks, Vijay