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General solutio of sin x+cos x=min(a in ...

General solutio of `sin x+cos x=min_(a in R) {1,a^(2)-4a+6}` is

A

`(npi)/(2)+(-1)^(n)(pi)/(4)`

B

`2npi+(-1)^(n)(pi)/(4)`

C

`npi+(-1)^(n+1)(pi)/(4`

D

`npi+(-1)^(n)(pi)/(4)-(pi)/(4)`

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