let `0ltphiltpi/2`, `x=sum_(n=0)^oocos^(2n)phi`, `y=sum_(n=0)^oosin^(2n)phi` and `z=sum_(n=0)^oocos^(2n)phisin^(2n)phi`

let 0

If 0 lt theta, phi lt (pi)/(2), x = sum_(n=0)^(oo)cos^(2n)theta, y=sum_(n=0)^(oo)sin^(2n)phi and z=sum_(n=0)^(oo)cos^(2n)theta*sin^(2n)phi then :

If 0

If =sum_(n=0)^(oo)cos^(2n)theta,quad y=sum_(n=0)^(oo)sin^(2n)phi,z=sum_(n=0)^(oo)cos^(2n)theta sin^(2n)phi, where 0

If x= sum_(n=0)^oo (Costheta)^(2n) , y= sum_(n=0)^oo (Sinphi)^(2n) , z= sum_(n=0)^oo (Cosphi)^(2n). (Sintheta)^(2n) Then which of the following is true ??

If x=sum_(n=0)^(oo) a^(n),y=sum_(n=0)^(oo)b^(n),z=sum_(n=0)^(oo)(ab)^(n) , where a,blt1 , then

If a=sum_(n=0)^(oo)x^(n),b=sum_(n=0)^(oo)y^(n),c=sum_(n=0)^(oo)(xy)^(n) where |x|,|y|<1 then