Solve the equation over the interval [0,2pi) 4cscx + 6= -2

1 answer:

3 0

$\bf 4csc(x)+6=-2\implies 4csc(x)=-8\implies csc(x)=\cfrac{-8}{4}\implies csc(x)=-2 \\\\\\ \cfrac{1}{sin(x)}=-2\implies \cfrac{1}{-2}=sin(x)\implies sin^{-1}\left( -\cfrac{1}{2} \right)=x\implies x= \begin{cases} \frac{7\pi }{6}\\\\ \frac{11\pi }{6} \end{cases}$

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