Question

Помогите пожалуйста cosa+sina=

Answer 1

Ответ:

$cosa+sina=\sqrt2\cdot \Big(\dfrac{1}{\sqrt2}\cdot cosa+\dfrac{1}{\sqrt2}\cdot sina\Big)=\\\\\\=\sqrt2\cdot \Big(sin\dfrac{\pi}{4}\cdot cosa+cos\dfrac{\pi}{4}\cdot sina\Big)=\sqrt2\cdot sin\Big(a+\dfrac{\pi}{4}\Big)$

Или:

$cosa+sina=\sqrt2\cdot \Big(\dfrac{1}{\sqrt2}\cdot cosa+\dfrac{1}{\sqrt2}\cdot sina\Big)=\\\\\\=\sqrt2\cdot \Big(cos\dfrac{\pi}{4}\cdot cosa+sin\dfrac{\pi}{4}\cdot sina\Big)=\sqrt2\cdot cos\Big(a-\dfrac{\pi}{4}\Big)$