Find All Solutions of the Following Equation in the Interval $[ 0,2 \pi )$

question 91

Multiple Choice

Find all solutions of the following equation in the interval $[ 0,2 \pi )$ .
$$\csc ^ { 2 } x = \cot x + 1$$

• A) \(x = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 4 \pi } { 3 }\)
• B) \(x = \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }\)
• C) \(x = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 }\)
• D) \(x = \frac { \pi } { 4 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 4 } , \frac { 3 \pi } { 2 }\)
• E) \(x = \frac { \pi } { 4 } , \frac { 4 \pi } { 3 } , \frac { 11 \pi } { 6 }\)

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