If `sin^3 x sin 3x = c_0-c_1 cos x + c_2 cos 2x +....c_n cos nx`

lim_(sin x sin3x)=c_(0)+c_(1)cos x+c_(2)cos2x+....+c_(n)cos nx

Prove : int sin x sin 2x sin 3x dx = - 1/48 ( 6 cos 2x + 3 cos 4x - 2 cos 6 x) + c

If sin^3x sin3x= sum_(n=0)^6 c_n cos^n x where c_0, c_1, c_2,...c_6 are constants. then find the value of c_4

1+ cos 2x+ cos4x + cos 6x= ............. A) 2 cos x cos 2x cos 3x B) 4 sin x cos 2x cos 3x C) 4 cos x cos 2x cos 3x D) 2 sin x cos 2x cos 3x

Solutions of the differential equations (dy)/(dx) + (y)/(x) = sin x is : a) x(y+cos x ) = sin x+ c b) x(y-cos x ) = sin x+c c) x( y cos x ) = sin x +c d) x(y-cos x) = cos x+ c

If sin ^(3) x sin 3x= sum _(m=0)^(n) c_(m) cos mx is an identity in x, where C_(0), C_(1),C_(2),…,C_(n) are constants and C_(n) ne 0, then the value of n is equal to-

2cosx-cos3x-cos5x= ............... A) 16 cos ^(3) x sin ^(2) x B) 16 sin^(2) x cos ^(2) x C) 4 cos ^(2) x sin ^(2) x D) 4 sin ^(2) x cos ^(2)x