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, 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 lt phi lt (pi)/(2) , x= sum_(n=0)^(oo) cos^(2n) phi ,y sum _(n=0)^(oo) sin ^(2n) phi and z = sum _(n=0) ^(oo) cos ^(2n) phi sin ^(2n) phi , 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 that (i) xyz=xy+z (ii) xyz=x+y+z

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

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 < theta,varphi < pi//2 prove that x z+y z-z=x ydot

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

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