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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`, where `0lttheta,varphi ltpi//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,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)^(oo) a^(n),y=sum_(n=0)^(oo)b^(n),z=sum_(n=0)^(oo)(ab)^(n) , where a,blt1 , 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 .

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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.

Evaluate S=sum_(n=0)^n(2^n)/((a^(2^n)+1) (where a>1) .

Prove that sum_(r=0)^(2n)(r. ^(2n)C_r)^2=n^(4n)C_(2n) .

p=sum_(n=0)^(oo) (x^(3n))/((3n)!) , q=sum_(n=1)^(oo) (x^(3n-2))/((3n-2)!), r = sum_(n=1)^(oo) (x^(3n-1))/((3n-1)!) then p + q + r =

RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
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  20. If x in R , find the minimum value of the expression 3^x+3^(1-x)dot

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