Question

Вычислите:
cos7П/12 × сosП/12

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Answer 1

$cos\dfrac{7\pi }{12}\cdot cos\dfrac{\pi}{12}=cos(\pi -\dfrac{5\pi }{12})\cdot cos\dfrac{\pi}{12}=-cos\dfrac{5\pi}{12}\cdot cos\dfrac{\pi}{12}=\\\\\\=-cos(\dfrac{\pi}{2}-\dfrac{\pi}{12})\cdot cos\dfrac{\pi}{12}=-sin\dfrac{\pi}{12}\cdot cos\dfrac{\pi}{12}=-\dfrac{1}{2}\cdot sin\Big(2\cdot \dfrac{\pi}{12}\Big)=\\\\\\=-\dfrac{1}{2}\cdot sin\dfrac{\pi}{6}=-\dfrac{1}{2}\cdot \dfrac{1}{2}=-\dfrac{1}{4}\\\\\\\\\star \; \; 2\, sin\alpha \cdot cos\alpha =sin(2\alpha )\; \; \; \star$