Question

if (x-1)^2+(y-1)^2+(z-1)^2=0 then value of x+y+z=?​

Answer 1

Step-by-step explanation:

Let x=tanA,y=tanB and z=tanC

Given x+y+z=xyz

⇒tanA+tanB+tanC=tanAtanBtanC

⇒tanA+tanB=−tanC+tanAtanBtanC

=−tanC(1−tanAtanB)⇒1−tanAtanBtanA+tanB=−tanC⇒tan(A+B)=tan(−C)

⇒A+B=nπ−C⇒A+B+C=nπ⇒2A+2B+2C=2nπ

⇒tan(2A+2B+2C)=tan2nπ=0

⇒[1−tan2Atan2B−tan2Btan2C−tan2Ctan2A][tan2A+tan2B+tan2C−tan2Atan2Btan2C]=0

⇒tan2A+tan2B+tan2C=tan2Atan2Btan2C⇒1−tan2A2tan