4sin-2pi-7-sec-pi-14-cot-pi-7-

Question Number 161254 by cortano last updated on 15/Dec/21

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

Commented by bobhans last updated on 15/Dec/21

P = \frac{4 \sin (\frac{2 π}{7}) \cos (\frac{π}{14}) + 1}{\cos (\frac{π}{14}) [\frac{\cos (\frac{π}{7})}{2 \sin (\frac{π}{14}) \cos (\frac{π}{14})}]}

P = \frac{4 \sin (\frac{2 π}{7}) \sin (\frac{π}{7}) + 2 \sin (\frac{π}{14})}{\cos (\frac{π}{7})}

P = \frac{- 2 (\cos (\frac{3 π}{7}) - \cos (\frac{π}{7})) + 2 \cos (\frac{3 π}{7})}{\cos (\frac{π}{7})}

P = \frac{2 \cos (\frac{π}{7})}{\cos (\frac{π}{7})} = 2

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