Question

докажите тождество
cosa+ sin a=1/2

Answer 1

$cos( \frac{\pi }{3}+a)\cdot cosa+sin(\frac{\pi }{3}+a)\cdot sina=\\\\= \Big [\, cos \alpha \cdot cos\beta +sin \alpha \cdot sin\beta =cos( \alpha - \beta )\, \Big ]=\\\\=cos\Big ((\frac{\pi }{3}+a)-a\Big )=cos\frac{\pi }{3}= \frac{1}{2}$