Question

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

Answer 1

`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^@`.