The number of real solutions of the equation `sin^(-1)(sum_(i=1)^oox^(i+1)-xsum_(i=1)^oo(x/2)^i)=pi/2-cos^(-1)(sum_(i=1)^oo(-x/2)^i-sum_(i=1)^oo(-x)^i)` lying in the interval `(-1/2,1/2)` is ____. (Here, the inverse trigonometric function `=sin^(-1)x` and `cos^(-1)x` assume values in `[pi/2,pi/2]` and `[0,\ pi]` , respectively.)

The number of real solution of the equation sin^(-1) (sum_(i=1)^(oo) x^(i +1) -x sum_(i=1)^(oo) ((x)/(2))^(i)) = (pi)/(2) - cos^(-1) (sum_(i=1)^(oo) (-(x)/(2))^(i) - sum_(i=1)^(oo) (-x)^(i)) lying in the interval (-(1)/(2), (1)/(2)) is ______. (Here, the inverse trigonometric function sin^(-1) x and cos^(-1) x assume values in [-(pi)/(2), (pi)/(2)] and [0, pi] respectively)

The number of real solution of the equation sin^(-1) (sum_(i=1)^(oo) x^(i +1) -x sum_(i=1)^(oo) ((x)/(2))^(i)) = (pi)/(2) - cos^(-1) (sum_(i=1)^(oo) (-(x)/(2))^(i) - sum_(i=1)^(oo) (-x)^(i)) lying in the interval (-(1)/(2), (1)/(2)) is ______. (Here, the inverse trigonometric function sin^(-1) x and cos^(-1) x assume values in [-(pi)/(2), (pi)/(2)] and [0, pi] respectively)

If sum_(i=1)^(2n)cos^(-1)x_(i)=0 , then sum_(i=1)^(2n)x_(i) is :

sum_(i=1)^(oo)tan^(-1)((1)/(2r^(2)))=

sum_(m=1)^(32)m[sum_(k=1)^(6)sin2k(pi)/(7)-i cos2k(pi)/(7)]

sum_(i=1)^(oo)sum_(j=1)^(oo)sum_(k=1)^(oo)(1)/(2^(i+j+k)) is equal to

If sum_(i=1)^(2n)sin^(-1)x_(i)=n pi then find the value of sum_(i=1)^(2n)x_(i)

If sum_(i=1)^(2 n) cos ^(-1) x_(i)=0, then sum_(i=1)^(2 pi) x_(i)=