`cos^(-1)((1-x^(2n))/(1+x^(2n)))`

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

(d)/(dx) {Cos ^(-1) ""( x ^(2n)-1)/(x ^(2n) + 1) }=

lim_(x rarr1)((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^(2)),n in N, equals ^2nP_(n)(b)^(2n)C_(n)(c)(2n)!(d) none of these

Evaluate: inte^x(1+n x^(n-1)-x^(2n))/((1-x^n)sqrt(1-x^(2n)))dx

Let S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n , then

Let S_(n)(x)=(x^(n-1)+(1)/(x^(n-1)))+2(x^(n-2)+(1)/(x^(n-2)))+"....."+(n-1)(x+(1)/(x))+n , then

cos x*cos2x*cos4x......cos(2^(n-1)x)=(sin2^(n)x)/(2^(n)sin x)AA n in N

Let the co-efficients of x^(n) In (1+x)^(2n) and (1+x)^(2n-1) be P& Qrespectively,then ((P+Q)/(Q))^(5)=

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

int_(-pi//2)^(pi//2)(sin^(2n-1)x)/(1+cos^(2n)x)dx=