Question

what is the general solution for sinx+cosx = 1

Answer 1

divide both sides by\[\frac{ 1 }{ \sqrt{2}}\]

Answer 2

aliter
sinx - (1-cosx) = 0
2sin(x/2)cos(x/2) -2(sin(x/2))^2 =0
2sin(x/2) * (sin(x/2) -cos(x/2)) =0
thus sin(x/2) = 0 or (sin(x/2) -cos(x/2)) =0 ==> tan(x/2) =1
hence further..

Answer 3

if sin(x/2) = 0
then
x/2 = n(pi) where n is an integer...
or x = 2npi

Answer 4

if tan(x/2) =1 = tan(pi/4)
then x = mpi +(pi/4) m is any integer