##x = 2npi and x = (4n+1)pi/2 n = 0 +-1 +-2 +-3. …##

The given equation is equivalent to

##1/sqrt 2 sin x+ 1/sqrt 2 cosx=1/sqrt 2##.

This can be written as

##cos (x-pi/4) = cos (pi/4)##

The general solution of this equation ls

##x-.pi/4=2npi+-pi/4 n = 0 +-1 +-2 …##

So ##x = 2npi and x = (4n+1)pi/2 n = 0 +-1 +-2 +-3. …##