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

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

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Answer 1 · 2016-07-08T10:50:32

#x=210^@, or, 330^@#.

Explanation:

#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^2x+2cscx=0# and find all solutions in the interval #0<=x<360#?

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