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Question Number 143890 by pandu last updated on 19/Jun/21

$$ifa+b+c=\pi$$$$tanA+tanB+tanC=tanA.tanB.tanC$$$$\mathrm{FAILED}\mathrm{TO}\mathrm{CALCULATE}$$

Answered by justtry last updated on 19/Jun/21

Answered by bobhans last updated on 19/Jun/21

$$\mathrm{a}+\mathrm{b}=\pi -\mathrm{c}$$$$\Rightarrow \frac{\tan \mathrm{a}+\tan \mathrm{b}}{1-\tan \mathrm{a}.\tan \mathrm{c}}=-\tan \mathrm{c}$$$$\Rightarrow \tan \mathrm{a}+\tan \mathrm{b}=-\tan \mathrm{c}+\tan \mathrm{a}\tan \mathrm{b}\tan \mathrm{c}$$$$\Rightarrow \tan \mathrm{a}+\tan \mathrm{b}+\tan \mathrm{c}=\tan \mathrm{a}.\tan \mathrm{b}.\tan \mathrm{c}$$

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