JEE Main 202125 Feb, Morning shiftMathematicsMediumSequence and Series179× since 2002If 0<θ,ϕ<π2,x=∑n=0∞cos2nθ,y=∑n=0∞sin2nϕ0 < \theta ,\phi < {\pi \over 2},x = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta } ,y = \sum\limits_{n = 0}^\infty {{{\sin }^{2n}}\phi }0<θ,ϕ<2π,x=n=0∑∞cos2nθ,y=n=0∑∞sin2nϕ and z=∑n=0∞cos2nθ.sin2nϕz = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta .{{\sin }^{2n}}\phi }z=n=0∑∞cos2nθ.sin2nϕ then :AOption A. xy −-− z = (x + y)zBOption B. xyz = 4COption C. xy + z = (x + y)zDOption D. xy + yz + zx = zCheckSkip · show solution
