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`

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 ________

Suppose sin^(3)x sin3x=sum_(m=0)^(n) C_(m) cos mx is an idedntity in x , where C_(0),….C_(n) are constant and C_(n)ne0 then the value of n is ___________

If C_(0), C_(1), C_(2),..., C_(n) are binomial coefficients in the expansion of (1 + x)^(n), then the value of C_(0) + (C_(1))/(2) + (C_(2))/(3) + (C_(3))/(4) +...+ (C_(n))/(n+1) is

If (1+x)^n=sum_(r=0)^n C_r x^r , then prove that C_1+2C_2+3C_3+....+n C_n=n2^(n-1)dot .

If (1+x)^n=c_0+c_1x+c_2x^2+...+c_nx^n then the value of c_0+3c_1+5c_2+....+(2n+1)c_n is-

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 dot

If (1+x)^n = C_0 + C_1x + C_2x^2 + ……..+C_n.x^n then find C_1 - C_3 + C_5 + ……

If C_o C_1, C_2,.......,C_n denote the binomial coefficients in the expansion of (1 + x)^n , then the value of sum_(r=0)^n (r + 1) C_r is

If sin x+cosec\ x=2, then write the value of sin^n x+cos e c^n xdot

If (1+x)^n = C_0 + C_1x + C_2x^2 + ……..+C_n.x^n then find C_0 - C_2 + C_4 - C_6 + …….