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Question

If A,B and C are the angles of non-right angles triangle ABC, then find the value of ∣ ∣tanA111tanB111tanC∣ ∣

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Solution

A+B=πC
tan(A+B)=tanC
tanA+tanB1tanAtanB=tanC
tanA+tanB+tanC=tanAtanBtanC ....(1)
Consider, ∣ ∣tanA111tanB111tanC∣ ∣
Δ=tanAtanBtanCtanAtanC+1+1tanB
Δ=2 (by (1))

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