[" 22.If "x=sum_(n=0)^(oo)cos^(2n)theta,y=sum_(n=0)^(oo)sin^(2n)theta,z=sum_(n=0)^(oo)cos^(2n)theta sin^(2n)theta" and "0

For 0 lt theta lt ( pi )/(2) , if x = sum_(n=0)^(oo)cos^(2n) theta, y = sum_(n=0)^(oo) sin^(2n) theta ,z=sum_(n=0)^(oo)cos^(2n) theta sin^(2n) theta ,then :

If 0 lt theta lt pi/2, x = sum_(n=0)^(oo)cos^(2n) theta, y =sum_(n=0)^(oo)sin^(2n)theta , and z=sum_(n=0)^(oo) cos^(2n)theta sin^(2n) theta then show that (i) xyz=xy+z (ii) xyz=x+y+z

If xsum_(n=0)^(oo)cos^(2n)theta,y=sum_(n=0)^(oo)sin^(2n)thetaandz=sum_(n=0)^(oo)cos^(2n)thetasin^(2n)theta,ltthetalt(pi)/(2), then show that xyz = x + y + z.

If x= sum_(n=0)^(oo) cos ^(2n)theta , y = sum _(n=o) ^(oo) sin ^(2n)theta, z= sum _(n=0)^(oo) cos ^(2n)theta.sin ^(2n)theta and 0 lt theta lt (pi)/(2) then-

"For "0ltthetalt(pi)/(2) , if x=sum_(n=0)^(oo)cos^(2n)theta,y=sum_(n=0)^(oo)sin^(2n)phi,z=sum_(n=0)^(oo)cos^(2n)thetasin^(2n)phi , then

If 0 lt theta lt pi/2, x= sum_(n=0)^(oo) cos^(2n) theta, y= sum_(n=0)^(oo) sin^(2n) theta and z=sum_(n=0)^(oo) cos^(2n) theta* Sin^(2n) theta , then show xyz=xy+z .

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 :