(n+1)sin^(-1)(2x)/(1+x^(2))quad [NCERT]

Iff(x)=2tan^(-1)x+sin^(-1)((2x)/(1+x^(2))),x>. The n,f(5) is equal to

f (x) = lim _(x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +1),n in N and g (x) =tan ((1)/(2)sin ^(-1)((2f (x))/(1+f ^(2) (x)))), then lim_(x to -3) ((x ^(2) +4x +3))/(sin (x+3) g (x)) is equal to:

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

If (sin^(-1)x+sin^(-1)y)(sin^(-1)Z+sin^(-1)w)=pi^(2) and n_(1),n_(2),n_(3),n_(4) in N value of |(x^(n1),y^(n2)),(z^(n)3,w^(n4))| cannot be equal to

If (sin^(-1)x+sin^(-1)y)(sin^(-1)Z+sin^(-1)w)=pi^(2) and n_(1),n_(2),n_(3),n_(4) in N value of |(x^(n1),y^(n2)),(z^(n)3,w^(n4))| cannot be equal to

If quad sin^(-1)x_(1)+sin^(-1)x_(2)++sin^(-1)x_(n) =1 then find the value of (x_(1)^(1)+x_(3)^(3)+x_(5)^(5)+...(m+1)terms)/(x_(2)^(2)+x_(4)^(4)+x_(6)^(6)+... mterms )