If `x=asecthetacosvarphi,\ \ y=bsecthetasinvarphi` and `z=ctantheta` , show that `(x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(c^2)=1`

If x=asecthetacosphi , y=secthetasinphiandz=ctantheta ,show that (x^(2))/(a^(2))+(y^(2))/(b^(2))-(z^(2))/(c^(2))=1 .

If x=asecthetacosvarphi , y=bsecthetasinvarphi and z=ctantheta , then (x^2)/(a^2)+(y^2)/(b^2)= (a) (z^2)/(c^2) (b) 1-(z^2)/(c^2) (c) (z^2)/(c^2)-1 (d) 1+(z^2)/(c^2)

If x = a sec A cos B, y = b sec A sin B and z = c tan A, show that : (x^(2))/ (a^(2)) + (y^(2))/ (b^(2)) - (z^(2))/(c^(2)) = 1

Show that |{:(x,y,z),(2x+2a,2y+2b,2z+2c),(a,b,c):}|=0

Let a ,b , c be real numbers. The following system of equations in x ,y and z (x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(a^2)=1,(x^2)/(a^2)-(y^2)/(b^2)+(z^2)/(a^2)=1,-(x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(a^2)=1 has a. no solution b. unique solution c. infinitely many solutions d. finitely many solutions

If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

If z= x + yi and |2z + 1| = |z- 2i| , show that 3(x^(2) + y^(2)) + 4(x-y)=3

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

If x+y+z=1a n dx ,y ,z are positive, then show that (x+1/x)^2+(y+1/y)^2+(z+1/z)^2>(100)/3