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

Prove the followings : If tan^(-1)((yz)/(xr))+tan^(-1)((zx)/(yr))+tan^(-1)((xy)/(zr))=pi/2 then x^(2)+y^(2)+z^(2)=r^(2) .

If y=sum_(r=1)^(x) tan^(-1)((1)/(1+r+r^(2))) , then (dy)/(dx) is equal to

If z=(i)^(i)^(i) where i=sqrt(-1),t h e n|z| is equal to 1 b. e^(-pi//2) c. e^(-pi) d. none of these

Prove the followings : If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi then x+y+z=xyz .

If x^(2)+y^(2)+z^(2)-2xyz=1 , then the value of (dx)/(sqrt(1-x^(2)))+(dy)/(sqrt(1-y^(2)))+(dz)/(sqrt(1-z^(2))) is equal to………..

x≥0,y≥0,z≥0 and tan^(-1) x+tan^(-1) y+tan^(-1) z=k , the possible value(s) of k if x^2 + y^2+z^2 = 1, & \ x+y+z=sqrt(3) , then

x≥0,y≥0,z≥0 and tan^(-1) x+tan^(-1) y+tan^(-1) z=k , the possible value(s) of k if x+y+z=xyz , then

x≥0,y≥0,z≥0 and tan^(-1) x+tan^(-1) y+tan^(-1) z=k , the possible value(s) of k if xy+yz+zx=1 , then

If x, y, z are in A.P. and tan^(-1)x , tan^(-1)y and t a n^(-1)z are also in A.P., then (1) 2x""=""3y""=""6z (2) 6x""=""3y""=""2z (3) 6x""=""4y""=""3z (4) x""=""y""=""z

If m^(th), n^(th) and p^(th) terms of an A.P and G.P be equal and be respectively x,y, z then………...................................................... a ) x^(y).y^(z).z^(x) = x^(z).Y^(x).z^(y) b ) (x-y)^(x).(y-z)^(y)= (z-x)^(z) c ) (x-y)^(z) (y-z)^(x)= (z-x)^(y) d ) None of these