#1+sin^2(x) = 3sin(x)cos(x)#, #tan(x)!=1/2#
#=> (sin^2(x)+cos^2(x))+sin^2(x) = 3sin(x)cos(x)#
#=> cos^2(x) + 2sin^2(x) = 3sin(x)cos(x)#
#=> cos^2(x)-3sin(x)cos(x)+2sin^2(x) = 0#
#=> (cos(x)-sin(x))(cos(x)-2sin(x)) = 0#
#=> cos(x)-sin(x) = 0# or #cos(x) - 2sin(x) = 0#
As the second equation may be expressed as #sin(x)/cos(x)=1/2#, violating our initial condition of #tan(x)!=1/2#, we will only focus on the first.
#cos(x)-sin(x) = 0#
#=> cos(x) = sin(x)#
#:. x = pi/4+pik#, #k in ZZ#