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

Let a,b,c be the 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 abc=1, then find ((x^(2))/(x^(2)-zy)+(y^(2))/(y^(2)-zx)+(z^(2))/(z^(2)-xy))

if (x)/(a^(2)-b^(2))=(y)/(b^(2)-c^(2))=(z)/(c^(2)-a^(2)) , then prove that x+y+z=0.

a(y+z)=x,b(z+x)=y,c(x+y)=z prove that (x^(2))/(a(1-bc))=(y^(2))/(b(1-ca))=(z^(2))/(c(1-ab))

If log x(log x)/(a^(2)+ab+b^(2))=(log y)/(b^(2)+bc+c^(2))=(log z)/(c^(2)+ca+a^(2)) then x^(a-b)*y^(b-c)*z^(c-a)=

(x^(2))/(by + cz) = (y^(2))/(ax + cz)= (z^(2))/(ax + by)=1 find (x)/(x+a) + (y)/(y+a) + (z)/(z+c) = ?

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