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Question Number 54472 by Tawa1 last updated on 04/Feb/19

$$\mathrm{If}\mathrm{A},\mathrm{B},\mathrm{C}\mathrm{are}\mathrm{angle}\mathrm{of}\mathrm{a}\mathrm{triangle},\mathrm{show}\mathrm{that}$$$$\mathrm{tanA}+\mathrm{tanB}+\mathrm{tanC}=\mathrm{tanA}\mathrm{tanB}\mathrm{tanC}$$

Answered by math1967 last updated on 04/Feb/19

$$A+B+C=\pi$$$$\Rightarrow A+B=\pi -C$$$$\Rightarrow tan(A+B)=tan(\pi -C)$$$$\Rightarrow \frac{tanA+\tan B}{1-tanA\tan B}=-tanC$$$$\therefore \tan A+\tan B+\tan C=\tan A\tan B\tan C$$

Commented by Tawa1 last updated on 04/Feb/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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