Question

In triangle ABC ,Evaluate tan A + tan ( B+C)
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Answer 1

Step-by-step explanation:

ANSWER

Since A,B,C are angle of triangle, A+B+C=π ...(i)

tan(A+B) =tan(π−C)=−tanC

tan(A+B) =

1−tanAtanB

tanA+tanB

=−tanC

Therefore, tanA+tanB=(−tanC)(1−tanAtanB)

tanA+tanB=−tanC+tanCtanAtanB

Therefore, tanA+tanB+tanC=tanAtanBtanC