Question

Solve the equation for 0 to 360 degrees.
cot^2 (x)-csc(x)=1

Answer 1

\[\frac{\cos ^2x}{\sin ^2x}-\frac{1}{\sin x}=1\]
\[\frac {\cos ^2x-\sin x}{\sin ^2x}=1\]
\[\frac{1-\sin ^2x-\sin x}{\sin ^2x}=1\]
\[1-\sin ^2x-\sin x=\sin ^2x\]
\[-2\sin ^2x-\sin x+1=0\]
\[\sin ^2x+\sin x-1=0\]
\[(2\sin x-1)(\sin x+1)=0\]
\[\sin x=\frac{1}{2} or \sin x=-1\]
\[x=30^{o}, 150^{o}, 270^{o}\]