If A+C=B, then tanAtanBtanC=
tanAtanB+tanC
tanBātanCātanA
tanA+tanCātanB
-(tanAtanB+tanC)
Finding the value of tanAtanBtanC :
Given, A+C=B
Apply ātanāon both sides,
tan(A+C)=tanB
ā(tanA+tanC)/(1ātanAtanC)=tanBāµtanA+B=(tanA+tanB)/(1ātanAtanB)
tanA+tanC=tanB(1ātanAtanC)
tanA+tanC=tanBātanAtanBtanC
ā“tanAtanBtanC=tanBātanAātanC
Hence, option (B) is correct.