`2sin(x) + csc(x) = 0` Find all the solutions of the equation in the interval `0,2pi)`.

Expert Answers
gsarora17 eNotes educator| Certified Educator

`2sin(x)+csc(x)=0`

`2sin(x)+1/sin(x)=0`

`(2sin^2(x)+1)/sin(x)=0`

solving above ,

`2sin^2(x)+1=0`

`2sin^2(x)=-1`

`sin^(2)x=-1/2`

`sin(x)=+-i/sqrt(2)`

Solutions for the range `0<=x<=2pi`  

No solutions