Question

sin(x) + 1 = cos(x)

Answer 1

sin(x) must be 0 in this case
sin(x)=0 x= 2pi
2nd case: cos(x) must be 0
sin(x) must be -1
x=3pi/2
therefore x=3pi/2 and x=2pi

Answer 2

sin(x)+sin^2x+cos^2(x)=cos(x)
since 1=sin^2x+cos^2
sin^2(x)+cos^2(x)=cos(x)-sin(x)
kind of unecessary step but
1=cos(x)-sin(x)
now think of this as 1=x-y
this is satisfied when x=1 and y=-1
so sin(x)=-1
sin^-1(-1)=x
x=3pi/2
cos(x)=1
cos^-1(1)=2pi
x=2pi
x=3pi/2