General solution of sinx+cosx=underset(a...

General solution of `sinx+cosx=underset(a in R)("min"){1,a^(2)-4a+6}` is

A

`(n pi)/( 2) + (- 1)^(n) (pi)/( 4) , n in Z`

B

` 2 n pi + (-1) ^(n) (pi)/( 4) , n in Z`

C

`n pi + (-1)^(n + 1) (pi)/(4) , n in Z`

D

` n pi + (- 1)^(n) (pi)/( 4) - (pi)/(4), n in Z`

Verified by Experts

The correct Answer is:

D

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