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The solution of the equation cos^2theta+...

The solution of the equation `cos^2theta+sintheta+1=0` lies in the interval

A

`(-(pi)/(4),(pi)/(4))`

B

`((pi)/(4),(3pi)/(4))`

C

`((3pi)/(4),(5pi)/(4))`

D

`((5pi)/(4),(7pi)/(4))`

Text Solution

Verified by Experts

The correct Answer is:
D
Given , `cos^(2)theta+sintheta+1=0`
`rArrsin^(2)theta-sintheta-2=0`
`rArr(sintheta+1)(sintheta-2)=0`
`rArrsintheta=-1="sin"(3pi)/(2)`
`[becausesinthetale1,so sinthetane2]`
`thereforetheta=(3pi)/(2)in((5pi)/(4),(7pi)/(4))`
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