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

Textbook Question

Chapter 5, 5.3 - Problem 31 - Precalculus (3rd Edition, Ron Larson).
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gsarora17 | (Level 2) Associate Educator

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`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

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