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Question Number 147651 by iloveisrael last updated on 22/Jul/21

$$\tan 1°+\tan 5°+\tan 9°+...+\tan 173°+\tan 177°=?$$

Commented by mr W last updated on 22/Jul/21

$$=45$$

Commented by iloveisrael last updated on 23/Jul/21

$$\mathrm{is}\mathrm{the}\mathrm{formula}$$$$\tan \alpha +\tan (60°-\alpha )+\tan (60°+\alpha )=3\tan \left(3\alpha \right)$$$$\mathrm{correct}?$$

Answered by mathmax by abdo last updated on 22/Jul/21

$$\mathrm{S}=\tan \left(\frac{\pi }{180}\right)+\tan \left(\frac{5\pi }{180}\right)+\tan \left(\frac{9\pi }{180}\right)+....+\tan \left(\frac{169\pi }{180}\right)+\tan \left(\frac{173\pi }{180}\right)+\tan \left(\frac{177\pi }{180}\right)$$$$\mathrm{S}=\tan \left(\frac{\pi }{180}\right)+\tan \left(\frac{5\pi }{180}\right)+\tan \left(\frac{9\pi }{180}\right)+...+\tan (\pi -\frac{9\pi }{180})+\tan (\pi -\frac{5\pi }{180})$$$$+\tan (\pi -\frac{\pi }{190})=0$$

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