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Question Number 28624 by Joel578 last updated on 28/Jan/18

Commented by Joel578 last updated on 28/Jan/18

$$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{expression}$$

Commented by Tinkutara last updated on 28/Jan/18

1?

Commented by matikzone.tk last updated on 28/Jan/18

$$piyekabarepakjoel?$$

Commented by Joel578 last updated on 29/Jan/18

$$baik$$

Answered by moxhix last updated on 28/Jan/18

$$\mathrm{show}:\mathrm{if}0<\alpha ,\beta ,\gamma <\pi ,\alpha +\beta +\gamma =\pi$$$$\mathrm{then}tan\alpha +tan\beta +tan\gamma =tan\alpha tan\beta tan\gamma .$$$$//$$$$tan\alpha =-tan(\pi -\alpha )=-tan(\beta +\gamma )$$$$=-\frac{tan\beta +tan\gamma }{1-tan\beta tan\gamma }$$$$tan\alpha (1-tan\beta tan\gamma )=-tan\beta -tan\gamma$$$$\therefore tan\alpha +tan\beta +tan\gamma =tan\alpha tan\beta tan\gamma .$$$$(\therefore \frac{tan\alpha +tan\beta +tan\gamma }{tan\alpha tan\beta tan\gamma }=1)$$$$//$$$$\mathrm{now}\mathrm{we}\mathrm{set}\alpha =\frac{2\pi }{2017},\beta =\frac{1006\pi }{2017},\gamma =\frac{1009\pi }{2017}.$$

Commented by Joel578 last updated on 29/Jan/18

$$thankyouverymuch$$

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