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If 12 cot^2theta-31cosectheta+32=0 then ...

If `12 cot^2theta-31cosectheta+32=0` then the value of `sintheta` is

A

`(3)/(5)or1`

B

`(2)/(3)or-(2)/(3)`

C

`(4)/(5)or(3)/(4)`

D

`+-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`12cot^(2)theta-31cosectheta+32=0`
`rArr12cos^(2)theta-31sintheta+32sin^(2)theta=0,sinthetane0`
`rArr12cos^(2)theta-12sintheta+20sin^(2)theta=1`
`rArr20sin^(2)theta-31sintheta+12=0 [becausecos^(2)theta=1-sin^(2)theta]`
`thereforesintheta=(31+-sqrt(31^(2)-4*20*12))/(2*20)`
`=(31+-sqrt(961-960))/(40)=(31+-1)/(40)`
`rArrsintheta=(4)/(5),(3)/(4)`
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