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Let A={theta in (-pi /2,pi):(3+2i sin th...

Let `A={theta in (-pi /2,pi):(3+2i sin theta )/(1-2 sin theta )` is purely imaginary }
Then the sum of the elements in A is

A

`pi`

B

`(3pi)/1`

C

`(2pi)/3`

D

`(5pi)/6`

Text Solution

Verified by Experts

The correct Answer is:
C
`(3+2 isin theta)/(1-2i sin theta)=((3+2isin theta)(1+2isin theta))/(1+4sin^(2)theta)`
`Re((3+2isintheta)/(2-2isin theta))=0implies3=4sin^(2)theta=0impliestheta=+-(pi)/3,(2pi)/3`
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