sin^2x+2sincosx-3cos^2x=0 sinx/2+cosx/2+sinx/2cosx/2=1 sinxcosx-sin^2x+sinx-cosx=0

sin^2x+2sincosx-3cos^2x=0 | /cos^2xtg^2x+2tgx-3=0tgx=yy^2+2y-3=0y=1y=-3Найдем х: 1) tgx=1x=pi/4+pik . k=z2) tgx=-3x=arctg (-3)+pik . k=z-sinx/2+cosx/2+sinx/2cosx/2=1 |/cosx/2tgx/2+1+sinx/2=1tgx/2+sinx/2=0 (sinx/2+sinx/2*cosx/2) /cosx/2=0 одз: 1) sinx/2+sinx/2*cosx/2=0sinx/2 (1+cosx/2)=01.sinx/2=0x/2=pikx=2pik. k=z2.cosx/2=-1x/2=pi/2+pikx=pi+2pik . k=z2) cosx/2≠0x≠pi/2+pik . k=zОтвет: x=pik . k=z-sinxcosx-sin^2x+sinx-cosx=0 sinx (cosx-sinx) — (cosx-sinx)=0 (cosx-sinx) (sinx-1)=01) cosx-sinx=0 |/sinxctgx=1x=pi/4+pik . k=z2) sinx-1=0sinx=1x=pi/2+2pik . k=z