Question

sin(15°) - cos(15°) =
Решите​

Answer 1

Ответ:

$- \frac{ \sqrt{2} }{2 }$

вот ответ

Answer 2

Ответ:

$-\frac{\sqrt{2}}{2}$

Объяснение:

$sin15^0-cos15^0=sin(45^0-30^0)-cos(45^0-30^0)=\\\\=(sin45^0cos30^0-cos45^0sin30^0)-(cos45^0cos30^0+sin45^0sin30^0)=\\\\=(\frac{\sqrt{2}}{2}*\frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}*\frac{1}{2})-(\frac{\sqrt{2}}{2}*\frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}*\frac{1}{2})=\\\\=\frac{\sqrt{2}}{2}*\frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}*\frac{1}{2}-\frac{\sqrt{2}}{2}*\frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}*\frac{1}{2}=\\\\=-\frac{\sqrt{2}}{4}-\frac{\sqrt{2}}{4}=- \frac{2\sqrt{2}}{4}=- \frac{\sqrt{2}}{2}$