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Question Number 192282 by universe last updated on 14/May/23

$$findthevalueof$$$$\tan \frac{\pi }{9}+4\sin \frac{\pi }{9}=?$$

Answered by som(math1967) last updated on 14/May/23

$$tan20+4sin20$$$$\frac{sin20+4sin20cos20}{cos20}$$$$=\frac{sin20+2sin40}{cos20}$$$$=\frac{sin20+sin40+sin40}{cos20}$$$$=\frac{2sin30cos10+cos50}{cos20}$$$$=\frac{cos10+cos50}{cos20}$$$$=\frac{2cos30cos20}{cos20}$$$$=\sqrt{3}$$

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