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General solution of cosex =- is...

General solution of cosex =- is

A

`x=2npi+(-1)^(n)(7pi)/(6),ninZ`

B

`x=2npi+-(7pi)/(6),ninZ`

C

`x=npi+(-1)^(n)(7pi)/(6),ninZ`

D

`x=npi+-(-1)^(n)(7pi)/(6),ninZ`

Text Solution

Verified by Experts

The correct Answer is:
C
`cosecx=-2`
`rArrsinx=-(1)/(2)rArrsinx=-"sin"(pi)/(6)`
`rArrsinx=sin(pi+(pi)/(6))orsin(2pi-(pi)/(6))`
`[becausesinx` is negative in 3rd and 4 th quadrant or `sin(pi+theta)=-sintheta]`
`rArrsinx="sin"(7pi)/(6)or"sin"(11pi)/(6)`
Here , principal value is `x=(7pi)/(6)`
General solution, `x=npi+(-1)^(n)alpha`
`rArrx=npi+(-1)^(n)(7pi)/(6)" " [becausen in Z]`
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