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)

Answer 3

To evaluate the expression, let's break it down step by step:

1. Let's start by evaluating the trigonometric functions:

   • cos(2π/7) ≈ 0.6235
   • cot(pi/7) is the reciprocal of the tangent function: cot(pi/7) = 1 / tan(pi/7)
   • tan(pi/7) ≈ 0.8714
   • Therefore, cot(pi/7) = 1 / 0.8714 ≈ 1.1481
   • sin(2π/7) ≈ 0.7818

2. Now, substitute the values into the expression: cos(2π/7) × cot(pi/7) + sin(2π/7) ≈ 0.6235 × 1.1481 + 0.7818 ≈ 0.7155 + 0.7818 ≈ 1.4973

Therefore, the value of cos(2π/7) × cot(pi/7) + sin(2π/7) is approximately 1.4973.