Question

12cosx-5sinx=-13
решите уравнение

Answer 1

$12Cosx-5Sinx=-13\\\\5Sinx-12Cosx=13\\\\a=5;b=12\\\\\sqrt{a^{2}+b^{2}}=13\\\\13(\frac{5}{13}Sinx-\frac{12}{13}Cosx)=13\\\\\frac{5}{13}=Cos\alpha;\alpha=arcCos\frac{5}{13}\\\\\frac{12}{13}=Sin\alpha\\\\13(SinxCos\alpha-CosxSin\alpha)=13\\\\Sin(x-\alpha)=1\\\\x-\alpha=\frac{\pi }{2}+2\pi n,nez\\\\x=\alpha+\frac{\pi }{2}+2\pi n,nez\\\\x=arcCos\frac{5}{13}+\frac{\pi }{2}+2\pi n,nez$