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

If x=costheta+isintheta Prove that (x^(2n)-1)/(x^(2n)+1)=itantheta

If z+1//z=2costheta, prove that |(z^(2n)-1)//(z^(2n)+1)|=|tanntheta|

If x and y are positive real numbers and m, n are any positive integers, then Prove that (x^n y^m)/((1+x^(2n))(1+y^(2m))) lt =1/4

If x satisfies x^(2)-2x cos theta +1=0 , then the value of x^(n)+((1)/(x^n)) is

If f(x)=(h_1(x)-h_1(-x))(h_2(x)-h_2(-x))... (h_(2n+1)(x)-h_(2n+1)(-x)a n df(200)=0, then prove that f(x) is many one function.

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

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

Prove that (1+costheta+isintheta)^(n)+(1+costheta-isintheta)^(n)=2^(n+1)cos^(n)((theta)/(2))cos((ntheta)/(2))

If costheta[(costheata, sintheta), (-sintheta, costheta)]+sintheta[(x, -costheta), (costheta, x)]=I_(2) . Find x.

If x_1 and x_2 are the real and distinct roots of a x^2+b x+c=0, then prove that lim_(n->x_1){1+"sin"(a x^2+b x+c)}^(1/(x-x_1))=e^(a(x_1-x_2))