sin 2x+2cos 2x =1

2sinxcosx+2(cosx)^2-2(sinx)^2-(cosx)^2-(sinx)^2=0

2sinxcosx+(cosx)^2-3(sinx)^2=0 |:(cosx)^2 не=0

2tgx+1-3(tgx)^2=0|*(-1)                x не=П/2+Пn,n принадлежит Z

3(tgx)^2-2tgx-1=0 |tgx=t

3t^2-2t-1=0

D=(-2)^2-4*3*(-1)=16

t1=(2+4)/6=1                                        t2=(2-4)/6=-1/3

tgx=1                                                   tgx=-1/3

x=П/4+Пn,n принадлежит Z                   x=-arctg 1/3 + Пk,k принадл.Z