##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. …##