This basic equation deploys in two independent equations.


First equation is

    cos(x) + sin(x) = 0.


It is equivalent to 

    cos(x) = -sin(x)

    tan(x) = -1


Its general solution is

    x =  = .     (1)



Second equation is 

    1 - 2sin(x) = 0,

which is the same as

    sin(x) = .


Its general solution is

    x =   and  x = .    (2)



ANSWER.  The general solution of the given equation is the union of these sets (1) and (2)

         x =   and  x = ,  x = .