Question

cos(2pi/7)×ctg(pi/7)+sin(2pi/7)

Answer 1

$cos\dfrac{2\pi}{7}\cdot ctg\dfrac{\pi}{7}+sin\dfrac{2\pi}{7}=cos\dfrac{2\pi}{7}\cdot \dfrac{cos\frac{\pi}{7}}{sin\frac{\pi}{7}}+sin\dfrac{2\pi}{7}=\\\\\\=\dfrac{cos\frac{2\pi}{7}\cdot cos\frac{\pi}{7}+sin\frac{2\pi}{7}\cdot sin\frac{\pi}{7}}{sin\frac{\pi}{7}}=\dfrac{cos(\frac{2\pi}{7}-\frac{\pi}{7})}{sin\frac{\pi}{7}}=\dfrac{cos\frac{\pi}{7}}{sin\frac{\pi}{7}}=ctg\dfrac{\pi}{7}$

Answer 2

Приведем к общему  знаменателю выражение, получим

cos(2π/7)×ctg(π/7)+sin(2π/7) =(cos(2π/7)×cos(π/7)+(sin(2π/7))*( sin(π/7))/sin(π/7)=

(cos(2π/7-π/7))/( sin(π/7)=ctg(π/7)