Предмет: Математика, автор: hakass

Решите уравнения sin(3x+pi/4)=

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Автор ответа: Trover

0

Применим формулу половинного угла, затем формулы приведения. $sinleft(3x+fracpi4right)=sinleft(fracpi4+3xright)=sqrt{frac{1-cosleft(fracpi2+6xright)}2}=sqrt{frac{1+sin6x}2}=\=sqrt{frac{sin^23x+2sin3xcos3x+cos^23x}2}=sqrt{frac{(sin3x+cos3x)^2}2}=frac{sin3x+cos3x}{sqrt2}$

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