How do you find all solutions of the equation in the interval $[0,2pi)$ given $3csc^2 5x=-4$ ?

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Answer 1 · 2018-02-07T07:46:14

No solution.

As $3csc^2 5x=-4$

$csc^2 5x=-4/3$

or $(cscx)^2=-4/3$

As square of a ratio cannot be negative,

it has no solution.

How do you find all solutions of the equation in the interval [0,2pi)[0,2pi) given 3csc^2 5x=-43csc^2 5x=-4?