If `x=sum_(n=0)^oocos^(2n)theta,y=sum_(n=0)^oosin^(2n)varphi,z=sum_(n=0)^oocos^(2n)thetasin^(2n)varphi,w h e r e0

If x=sum_(n=0)^oocos^(2n)theta,y=sum_(n=0)^oosin^(2n)varphi,z=sum_(n=0)^oocos^(2n)thetasin^(2n)varphi , where 0lttheta,varphi ltpi//2 prove that x z+y z-z=x ydot

"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 =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 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 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.

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 :

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 then xyz=?

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

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