If sin3 x sin 3x=∑nm=0cm cos mx where c0,c1,c2.⋯⋯,cn are constants and cn≠0, then the value of n is
6
sin3 x sin 3x=14(3 sin x−sin 3x)sin 3x=38.2 sin x sin 3x −18.2 sin2 3x=38(cos 2x−cos 4x)−18(1−cos 6x)=−18+38 cos 2x−38cos 4x+18cos 6x ....(i)
and ∑nm=0cm cos mx=c0+c1 cos x+c2 cos 2x +c3 cos 3x+.....+cn cos nx ......(ii)
Comparing both sides of (i) and (ii), we get n = 6