ПОЖАЛУЙСТА . 50 БАЛЛОВ. Created by fedcenkoana875. matematika-ru

ПОЖАЛУЙСТА . 50 БАЛЛОВ...

NNNLLL54

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Ответ:

$\displaystyle cos\frac{\pi}{5}\cdot cos\frac{2\pi}{5}=\frac{1}{2}\cdot \Big(cos\frac{3\pi}{5}+cos\frac{\pi}{5}\Big)=\frac{1}{2}\cdot \Big(cos(\pi -\frac{2\pi }{5})+cos\dfrac{\pi }{5}\Big)=\\\\\\=\frac{1}{2}\cdot \Big(-cos\frac{2\pi}{5}+cos\frac{\pi}{5}\Big)=\frac{1}{2}\cdot \Big(-\frac{\sqrt5-1}{4}+\frac{\sqrt5+1}{4}\Big)=\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}$

$\star \ \ cos\dfrac{\pi}{5}=cos36^\circ =\dfrac{\sqrt5+1}{4}\ \ ,\ \ \ cos\dfrac{2\pi}{5}=cos72^\circ =\dfrac{\sqrt5-1}{4}\ \ \star$

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bel72777

Ответ:

Пошаговое объяснение:

cos π/5 ·cos (2π)/5=(2sin π/5 ·cos π/5 ·cos (2π)/5)/(2sin π/5)=(sin (2π)/5 ·cos (2π)/5)/(2cos π/5)=(sin72° ·cos72°)/(2cos36°)=(sin144°)/(4cos36°)=(cos36°)/(4cos36°)=1/4

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