MathDB

5

Part of 1969 German National Olympiad

Problems(1)

sin 5x = 16 sin x sin (x -\pi/5) sin (x +\pi/5) sin (x -2\pi/5) sin (x +2\pi/5)

Source: 1968-69 Germany R4 12.5

10/13/2024
Prove that for all real numbers xx holds: sin⁡5x=16sin⁡x⋅sin⁡(x−π5)⋅sin⁡(x−2π5)sin⁡(x+2π5)\sin 5x = 16 \sin x \cdot \sin \left(x -\frac{\pi}{5} \right) \cdot \sin\left(x -\frac{2\pi}{5} \right) \sin \left(x +\frac{2\pi}{5} \right)
trigonometryalgebra