Question 951508
Find all solutions, showing the work, of the equation on [0,2π].
1 = cot^2 + csc x
{{{1=cot^2(x)+cscx}}}
{{{1=cos^2(x)/sin^2(x)+1/sinx}}}
lcd:sin^2(x)
{{{sin^2(x)=(cos^2(x)+sinx)}}}
{{{sin^2(x)=1-sin^2(x)+sinx}}}
2sin^2(x)-sinx-1+0
(2sinx+1)(sinx-1)=0
..
2sinx+1=0
sinx=-1/2
x=π/6,11π/6
or
sinx-1=0
x=0,π,2π