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Question

If A+B+C=180o , and tanA+tanB+tanC=ktanAtanBtanC, then value of k is

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Solution

Given that A+B+C=180

A+B=180C

Applying tan on both sides

tan(A+B)=tan(180C)

tanA+tanB1tanAtanB=tanC

tanA+tanB=tanC(1tanAtanB)

tanA+tanB=tanC+tanAtanBtanC

tanA+tanB+tanC=tanAtanBtanC

k=1

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