Q

# Help me answer: - Trigonometry - JEE Main-5

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)

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

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As we have learned

Graph of Trigonometric Ratios -

- 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)

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

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