Home
Class 12
MATHS
Suppose sin^3xsin3x=sum(m=0)^n Cmcosm x...

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 ________

Text Solution

Verified by Experts

The correct Answer is:
6
Given, `sin^(3) x sin 3x = underset(m=0)overset(n)SigmaC_(m) cos nx` is an identity in x,
Where, `C_(0), C_(1), …, C_(n)` are constants.
`sin^(3) x sin 3x = (1)/(4) {3 sin x - sin 3x}.sin 3x` ltbgt `=(1)/(4)((3)/(2).2sin x. sin 3x-sin^(2)3x)`
`=(1)/(4){(3)/(2)(cos2x - cosx)-(1)/(2)(1-cos 6x)}`
`=(1)/(8)(cos 6x + 3cos 2x - 3 cos x - 1)`
`therefore` On comparing both sides, we get n = 6
Promotional Banner

Similar Questions

Explore conceptually related problems

If cos^3xsin2x=sum_(r=0)^n a_xsin(r x),AAx in R then

Find the sum sum_(r=0)^n^(n+r)C_r .

Prove that sum_(r=0)^ssum_(s=1)^n^n C_s^ s C_r=3^n-1.

Find the sum 3^n C_0-8^n C_1+13^n C_2 - 18^n C_3+..

If f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0 and f(0)=1 is continuous at x=0 then the value of m+n is a. 2 b. 3 c. -3 d. 7

Prove that sum_(r=0)^n^n C_rsinr xcos(n-r)x=2^(n-1)sin(n x)dot

If x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in N , then find the minimum value of a+b+c

If sin^2x-2sinx-1=0 has exactly four different solutions in x in [0,npi] , then value/values of n is/are (n in N) 5 (b) 3 (c) 4 (d) 6

If the sum of n terms of an A.P is cn (n-1)where c ne 0 then the sum of the squares of these terms is

If (1+x)^n=sum_(r=0)^n^n C_r , show that C_0+(C_1)/2++(C_n)/(n+1)=(2^(n+1)-1)/(n+1) .