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 z=(costheta+isintheta) , show that z^(n)+(1)//(z^(n))=2cosntheta and z^(n)-(1)(z^(n))=2isinntheta

If x+iy = (3)/(2+costheta+ isintheta) prove that x^(2)+y^(2)=4x-3

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

choose the correct pair of statement : (i) (costheta+isintheta)^(n)=cosntheta+isinntheta , x is an integer (ii) (sintheta+icostheta)^(n)=sinntheta+icosthetantheta , n is an integer (iii) If z=costheta+isintheta , then z^(-1)=costheta-isintheta (iv)(z+barz)/(2)=Re(z)

Prove that cos^(-1)((1-x^(2n))/(1+x^(2n)))=2tan^(-1)x^n ,0 lt x lt oo

Prove that lim_(xrarr0) ((1+x)^(n) - 1)/(x) = n .

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 S_(n)=(x+y)+(x^(2)+xy+y^(2))+(x^(3)+x^(2)y+y^(2)x+y^(3))+…n terms then prove that (x-y)S_(n)=[(x^(2)(x^(n)-1))/(x-1)-(y^(2)y^(n)-1)/(y-1)] .