Question

How do you find all solutions of the equations `2sinx+cscx=0` in the interval `[0,2pi)`?

Answer 1

No solution

Explanation:

`2sinx+cscx=0` can be written as

`2sinx+1/sinx=0` and multiplying by `sinx` we get

`2sin^2x+1=0`

But LHS can never be `0`,

hence we donot have any solution.

This can also be checked from the graph of `2sinx+cscx`, which never has a value of `0`.
graph{2sinx+cscx [-10, 10, -5, 5]}