Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 28515 by beh.i83417@gmail.com last updated on 26/Jan/18

Answered by mrW2 last updated on 26/Jan/18

$$\tan 20-\tan 40+\tan 80$$$$=\tan 20-\tan (60-20)+\tan (60+20)$$$$=\tan 20-\frac{\sqrt{3}-\tan 20}{1+\sqrt{3}\tan 20}+\frac{\sqrt{3}+\tan 20}{1-\sqrt{3}\tan 20}$$$$=\tan 20+\frac{\tan 20-\sqrt{3}}{1+\sqrt{3}\tan 20}+\frac{\tan 20+\sqrt{3}}{1-\sqrt{3}\tan 20}$$$$=\tan 20+\frac{8\tan 20}{1-{3\tan }^{2}20}$$$$=3\times \frac{(3-{\tan }^{2}20)\tan 20}{1-{3\tan }^{2}20}$$$$=3\tan \left(3\times 20\right)$$$$=3\tan 60$$$$=3\sqrt{3}$$$$$$$$PS:$$$$\tan 3\alpha =\frac{\tan \alpha +\tan 2\alpha }{1-\tan \alpha \tan 2\alpha }=\frac{\tan \alpha +\frac{2\tan \alpha }{1-{\tan }^2\alpha }}{1-\tan \alpha \frac{2\tan \alpha }{1-{\tan }^2\alpha }}$$$$\tan 3\alpha =\frac{\tan \alpha (1-{\tan }^2\alpha )+2\tan \alpha }{1-{\tan }^2\alpha -{2\tan }^2\alpha }$$$$\Rightarrow \tan 3\alpha =\frac{(3-{\tan }^2\alpha )\tan \alpha }{1-{3\tan }^2\alpha }$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com