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What is the solution set of the equation  \csc x > 1 in the interval [0,2 \pi ] ? 

  • Option 1)

    [0, 2\pi ]

  • Option 2)

    [0, 2\pi ]- \left \{ \pi \right \}

  • Option 3)

    [0, 2\pi ]- \left \{ \pi/2 , 3 \pi/2 \right \}

  • Option 4)

    [0, 2\pi ]- \left \{ \pi/2, \pi, 3 \pi /2 \right \}

 

Answers (1)

best_answer

As we have learned

Graph of Trigonometric Ratios -

graph 5

- wherein

This is the graph of y = \csc x

 

 As seen in the graph the graph is always on or above the line x = 1 or on below the linbe x =-1 

Thus  cosec x > 1 will be x \epsilon [0, 2\pi ]- \left \{ \pi/2 , 3\pi/2 \right \} because at x = \pi/2 , 3\pi/2 ; 

cosec x = 1 

 


Option 1)

[0, 2\pi ]

Option 2)

[0, 2\pi ]- \left \{ \pi \right \}

Option 3)

[0, 2\pi ]- \left \{ \pi/2 , 3 \pi/2 \right \}

Option 4)

[0, 2\pi ]- \left \{ \pi/2, \pi, 3 \pi /2 \right \}

Posted by

Himanshu

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