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=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 = 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

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

Let a ,b , c be the real numbers. The following system of equations in x ,y ,a n dz (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 x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2)(2y)/(1-y^2)(2z)/(1-z^2)dot

If x/a=y/b=z/c, then show that (x^3+a^3)/(x^2+a^2)+(y^3+b^3)/(y^2+b^2)+(z^3+c^3)/(z^2+c^2)=((x+y+z)^3+(a+b+c)^2)/((x+y+z)^2+(a+b+c)^2).

Without expanding,FIND "Delta"=|(((a-x)^2),((a-y)^2),((a-z)^2)),(((b-x)^2),((b-y)^2),((b-z)^2)),(((c-x)^2),((c-y)^2),((c-z)^2))|

If a x+b y+c z=p , then minimum value of x^2+y^2+z^2 is (p/(a+b+c))^2 (b) (p^2)/(a^2+b^2+c^2) (a^2+b^2+c^2)/(p^2) (d) ((a+b+c)/p)^2

Without expanding, show that "Delta"=|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|=2(a-b)(b-c)(c-a)(x-y)(y-z)(z-x)