How do you solve ${csc}^{2} x + 2 csc x = 0$ $csc^2x+2cscx=0$ and find all solutions in the interval $0 \leq x < 360$ $0<=x<360$ ?

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How do you solve ${csc}^{2} x + 2 csc x = 0$ $csc^2x+2cscx=0$ and find all solutions in the interval $0 \leq x < 360$ $0<=x<360$ ?

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Answer 1 · 2016-07-08T10:50:32

$x = 210^{\circ}, or, 330^{\circ}$ $x=210^@, or, 330^@$ .

Explanation:

${csc}^{2} x + 2 csc x = 0 .$ $csc^2x+2cscx=0.$
$rArr cscx(cscx+2)=0................(1)$
$rArr cscx=0,$ which is not possible , bcz., $AAx in RR-{kpi : kinZZ}$ =Domain of csc fun., $cscx in RR-(0,1).$

$:.$ By $(1)$ , $cscx=-2, i.e., sinx=-1/2=-sin30^@$

Since we have to keep $0<=x<360, x=180^@+30^@=210^@, or, x=360^@-30^@=330^@$

Hence, $x=210^@, or, 330^@$ .

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How do you solve ${csc}^{2} x + 2 csc x = 0$ $csc^2x+2cscx=0$ and find all solutions in the interval $0 \leq x < 360$ $0<=x<360$ ?

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How do you solve csc^2x+2cscx=0csc2x+2cscx=0csc^2x+2cscx=0 and find all solutions in the interval 0<=x<3600≤x<3600<=x<360?

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Explanation:

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How do you solve ${csc}^{2} x + 2 csc x = 0$ $csc^2x+2cscx=0$ and find all solutions in the interval $0 \leq x < 360$ $0<=x<360$ ?