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

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

Differentiate the following function with respect to x:cos^(-1)((1-x^(2n))/(1+x^(2n))),0

If y=cos^(-1)((x^(2n)-1)/(x^(2n)+1)))," then "(1+x^(2n))y_(1)=

Prove that: I_(n)=int_(0)^(oo)x^(2n+1)e^(-x^(2))dx=(n!)/(2),n in N

Differentiate ' cos^(^^)(-1)((1-x^(^^)(2n))/(1+x^(^^)(2n)),backslash backslash0

Prove that int(dx)/((1+x^(2))^(n))=(1)/(2(n-1))[(x)/((1+x^(2))^(n-1))+(2n-3)int(dx)/((1+x^(2))^(n-1))],n in N Hence,computer the value of int cos^(4)xdx

let f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1)

Prove that: sin(n+1)x sin(n+2)x+cos(n+1)x cos(n+2)x=c

Prove that cos x+^(n)C_(1)cos2x+^(n)C_(2)cos3x+....+^(n)C_(n)cos(n+1)x=2^(n)*(cos^(n)x)/(2)*cos((n+2)/(2))x