Suppose `sin^3xsin3x=sum_(m=0)^n C_mcosm x` is an identity in `x ,` where `C_0,C_1 ,C_n` are constants and `C_n!=0,` the the value of `n` is ________

Answer

6

Explanation

According to the given questions, we have to express L.H.S. in the form
`C_0 + C_1 cos x + C_2 cos 2x +… + C_n cos nx`
Now,
` sin ^(3) x sin 3 x = (3sin x - sin 3x)/( 4) sin 3x`
`" " = ( 3sin x sin 3x - sin ^(2)3x)/(4)`
`" " = ( 3(cos 2x -cos 4x ) - (1-cos 6x))/(8) `
Hence, `n=6`