find-the-value-of-tan-pi-9-4sin-pi-9-

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

f i n d t h e v a l u e o f

\tan \frac{π}{9} + 4 \sin \frac{π}{9} = ?

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

t a n 20 + 4 s i n 20

\frac{s i n 20 + 4 s i n 20 c o s 20}{c o s 20}

= \frac{s i n 20 + 2 s i n 40}{c o s 20}

= \frac{s i n 20 + s i n 40 + s i n 40}{c o s 20}

= \frac{2 s i n 30 c o s 10 + c o s 50}{c o s 20}

= \frac{c o s 10 + c o s 50}{c o s 20}

= \frac{2 c o s 30 c o s 20}{c o s 20}

= \sqrt{3}