Mathematics, 09.11.2019 15:31 xaguilar
Find all solutions to cosx cos3 x-sinx sine3x= 0 on the interval {0,2pi}
Answers: 2
![\bf cos(x)cos(3x)-sin(x)sin(3x)=0\implies cos(x+3x)=0 \\\\\\ cos(4x)=0\implies cos^{-1}[cos(4x)]=cos^{-1}(0)\implies 4x=cos^{-1}(0) \\\\\\ 4x= \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}\implies \begin{cases} 4x=\cfrac{\pi }{2}\implies &\measuredangle x=\cfrac{\pi }{8}\\\\ 4x=\cfrac{3\pi }{2}\implies &\measuredangle x=\cfrac{3\pi }{8} \end{cases}](/tpl/images/0367/0741/51aad.png)
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