If `x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n dz=c+c/(r^2)+c/(r^4)+oo,` prove that `(x y)/z=(a b)/c dot`

If |r| gt 1, x = a + a/r + a/r^(2) + .......... infty , y = b - b/r + b/r^(2) - ......... infty and z = c + c/r^(2) + c/r^(4) + ...... infty , then the value of (xy)/z =

If T_r=r(r^2-1), then find sum_(r=2)^oo1/Tdot

Prove that (r_(1) -r)/(a) + (r_(2) -r)/(b) = (c)/(r_(3))

If in Delta ABC, (a -b) (s-c) = (b -c) (s-a) , prove that r_(1), r_(2), r_(3) are in A.P.

C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangent at any point P on this hyperbola meet the straight lines b x-a y=0 and b x+a y=0 at points Qa n dR , respectively. Then prove that C QdotC R=a^2+b^2dot

If the ratio of the roots of a x ^2+2b x+c=0 is same as the ratios of roots of p x^2+2q x+r=0, then a. (2b)/(a c)=(q^2)/(p r) b. b/(a c)=(q^)/(p r) c. (b^2)/(a c)=(q^2)/(p r) d. none of these

With usual notations, in triangle A B C ,acos(B-C)+bcos(C-A)+c"cos"(A-B) is equal to(a) (a b c)/R^2 (b) (a b c)/(4R^2) (c) (4a b c)/(R^2) (d) (a b c)/(2R^2)

Let the incircle with center I of A B C touch sides BC, CA and AB at D, E, F, respectively. Let a circle is drawn touching ID, IF and incircle of A B C having radius r_2dot similarly r_2a n dr_3 are defined. Prove that (r_1)/(r-r_1)dot(r_2)/(r-r_2)dot(r_3)/(r-r_3)=(a+b+c)/(8R)

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r)) is equal to (a) pi (b) pi/2 (c) 0 (d) none of these

If a ,b ,c in R and equations a x^2+b x+c=0a n dx^2+2x+9=0 have a common a rot, then find a : b : c dot