Question

Решите уравнение
sinx+cosx=-1

Answer 1

$sinx+cosx=-1 \bigg|:\sqrt{2}\\ \frac{1}{\sqrt{2}}sinx+\frac{1}{\sqrt{2}}cosx=-\frac{1}{\sqrt{2}}\\ sinxcos \frac{\pi}{4}+sin \frac{\pi}{4}cosx=-\frac{1}{\sqrt{2}}\\ sin(x+\frac{\pi}{4})=-\frac{1}{\sqrt{2}}\\ \left [ \begin{gathered} x+\frac{\pi}{4}=-\frac{\pi}{4}+2 \pi k, k \in Z\\ x+\frac{\pi}{4}=-\frac{3\pi}{4}+2 \pi n, n \in Z \end{gathered} \right.$

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