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If x=sum(n=0)^oocos^(2n)theta,y=sum(n=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`

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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 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 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

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For 0 < varphigeqpi/2,ifx=sum_(n=0)^oocos^(2n)varphi,y=sum_(n=0)^oosin^(2n)varphi,t h e n (a) x y z=x z+y (b) x y z=x y+z (c) x y z=x+y+z (d) x y z=y z+x

If x=sum_(n=0)^ooa^n , y=sum_(n=0)^oob^n , z=sum_(n=0)^ooc^n , w h e r e ra ,b ,a n dc are in A.P. and |a|<,|b|<1,a n d|c|<1, then prove that x ,ya n dz are in H.P.

If a_n=sum_(r=0)^n1/(nC_r), then sum_(r=0)^n r/(nC_r) equals

Find the sum sum_(r=0)^n^(n+r)C_r .

Find the sum sum_(r=0)^n^(n+r)C_r .

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