Find `1//x+x=2costheta` , then prove that `x^n+1//x^n=2cosnthetadot`

If x+(1)/(x)=2costheta , then x^(n)+(1)/(x^(n)) is equal to

If x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1+sintheta) is equal to 1+x (b) 1-x (c) x (d) 1/x

If I_(n)=int(x^(n)dx)/(sqrt(x^(2)+a)) then prove that I_(n)+(n-1)/(n)al_(n-2)=(1)/(n)x^(n-1)*sqrt(x^(2)+a)

Using mathematical induction prove that x+4x+7x+......+(3n-2)x=(1)/(2)n(3n-1)x

Find the sum of the series 1+2x+3x^(2)+(n-1)x^(n-2) using differentiation.

Find the sum of the series 1+2x+3x^(2)+(n-1)x^(n-2)) using differentiation.

if n is a positive integer,find the co-efficient of x^(n) in the expansion of ((3x-2)^(n))/((1-x)^(2))

Prove that the coefficients of x^(n) in (1+x)^(2n) is twice the coefficient of x^(n) in (1+x)^(2n-1)