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The value of x in[-2pi,2pi] such that (...

The value of `x in[-2pi,2pi]` such that `(sinx+icosx)/(1+i),i=sqrt(-1)`, is purely imaginary ,are given by

A

`npi-(pi)/(4)`

B

`npi+(pi)/(4)`

C

`npi`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(sinx+icosx)/(1+i)=((1-i)(sinx+icosx))/((1+i)(1-i))`
`=(sinx+cosx+i(cosx-sinx))/(2)`
Which is purely imagi enary
`rArrsinx+cosx=0rArrtanx=-1`
`thereforex=npi-(pi)/(4)`
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