If `x+y+z=xyz`, prove by trignometry 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))`

If `x+y+z=xyz`, prove by trignometry that: `(2x)/(1-x^(2))+(2y)/(1-y^(

1.	If `x+y+z=xyz`, prove by trignometry 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))`
Answer» Let x=tanA, y=tanB, z=tanC Now, `x+y+z=xyz` `rArr x+y=-z+xyz` `=-z(1-xy)` `rArr (x+y)/(1-xy)=-z` `rArr (tanA+tanB)/(1-tanAtanB)=-tanC` `rArr tan(A+B)=tan(pi-C)` `rArr 2A+2B=2pi-2C` `rArr tan(2A+2B)=tan(2pi-2C)`