1)2(sinx+cosx)+sin2x+1=0 2(sinx+cosx)+(sinx+cosx)²=0 (sinx+cosx)(2+sinx+cosx)=0 sinx+cosx=0 sinx+sin(π/2-x)=0 2sinπ/4cos(x-π/4)=0⇒cos(x-π/4=0⇒x-π/4=π/2+πn⇒x=3π/4+πn 2+sinx+cosx=0 2+2sinπ/4cos(x-π/4)=0 2+√2cos(x-π/4)=0⇒cos(x-π/4)=-√2∉[-1;1]-нет решения 2)2sinxcosx+cos2x-1=0 2sinxcosx-2sin²x=0 /2cos²x≠0 tg²x-tgx=0 tgx(tgx-1)=0 tgx=0⇒x=πn tgx=1⇒x=π/4+πn 3)sin^4 x+cos^4 x=1 (1-cos2x)²/4+(1+cos2x)²/4=1 1-2cos2x+cos²2x+1+2cos2x+cos²2x=4 cos²2x=1 1+cos4x=2⇒cos4x=1⇒4x=2πn⇒x=πn/2