SOLUTION: Find all solutions, showing the work, of the equation on [0,2π]. 1 = cot^2 + csc x

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions, showing the work, of the equation on [0,2π]. 1 = cot^2 + csc x      Log On


   

Question 951508: Find all solutions, showing the work, of the equation on [0,2π].
1 = cot^2 + csc x
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find all solutions, showing the work, of the equation on [0,2π].
1 = cot^2 + csc x
1=cot%5E2%28x%29%2Bcscx
1=cos%5E2%28x%29%2Fsin%5E2%28x%29%2B1%2Fsinx
lcd:sin^2(x)
sin%5E2%28x%29=%28cos%5E2%28x%29%2Bsinx%29
sin%5E2%28x%29=1-sin%5E2%28x%29%2Bsinx
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