Find-the-value-of-4-sin-2pi-7-sec-pi-14-cot-pi-7-

Question Number 130465 by naka3546 last updated on 25/Jan/21

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

\frac{4 \sin (\frac{2 π}{7}) + \sec (\frac{π}{14})}{\cot (\frac{π}{7})}

Answered by Dwaipayan Shikari last updated on 26/Jan/21

\frac{4 s i n (\frac{2 π}{7}) c o s (\frac{π}{14}) s i n (\frac{π}{7}) + s i n (\frac{π}{7})}{c o s \frac{π}{7} c o s \frac{π}{14}}

= \frac{2 c o s \frac{π}{7} c o s \frac{π}{14} - 2 c o s \frac{3 π}{7} c o s \frac{π}{14} + s i n \frac{π}{14}}{c o s \frac{π}{7} c o s \frac{π}{14}}

= 2 + \frac{- c o s (\frac{7 π}{14}) - c o s (\frac{5 π}{14}) + s i n (\frac{π}{14})}{c o s \frac{π}{7} c o s \frac{π}{14}}

= 2 + \frac{- 0 + s i n (\frac{π}{14}) - s i n (\frac{π}{14})}{c o s \frac{π}{7} c o s \frac{π}{14}} = 2

Commented by naka3546 last updated on 26/Jan/21

thanks, sir .