Question

Решите уравнение
sinx+cosx=-1

Answer 1

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

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