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If (x-1)^2+(y-1)^2+(z-1)^2=0 then value of x+y+z=? |
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Answer» -STEP EXPLANATION:LET x=tanA,y=tanB and z=tanCGiven 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 |
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