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All the permissible value of b ,a=sin(2x...

All the permissible value of b ,a=sin(2x-b)if `a=0` and `x=S_(2)` is a subset of `(0, pi)` are given by

A

`b in (-n pi, 2npi), n in Z`

B

`b in (-n pi, 2pi - npi), n in Z`

C

`b in (-n pi, npi), n in Z`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`a=0 rArr sin (2 theta-b)=0`
`rArr 2 theta-b=n pi, n in Z`
`rArr theta=(n pi+b)/2, n in Z, S_(2)=(n pi +b)/2, n in Z`
`S_(2)` is subset of `(0, pi)`
`:. 0 lt (n pi +b)/2 lt pi, n in Z`
`:. 0 lt n pi +b lt 2pi rArr -n pi lt b lt -n pi +2pi`
`rArr b in (-n pi, 2pi-npi), n in Z`
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