Question

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

Answer 1

`\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} (7\pi )/(6)\\\\ (11\pi )/(6) \end{cases}`