sin2x+5(cosx+sinx+1)=0

sin2x+5(cosx+sinx+1)=0sin2x+1+5(cosx+sinx)+4=01)(2sinxcosx+sin²x+cos²a)+5(cosx+sinx)+4=0(cosx+sinx)²+5(cosx+sinx)+4=0cosx+sinx=tt²+5t+4=0D=25-16=9=3²t=(-5±3)/2t1=-4;t2=-12) sinx+cosx=√2(1/√2sinx+1/√2cosx)=√2sin(x+π/4)t€[-√2;√2]t1=-4¢[-√2;√2]3)√2sin(x+π/4)=-1sin(x+π/4)=-1/√2x+π/4=(-1)ⁿ(-π/4)+πnx=-π/4+(-1)ⁿ(-π/4)+πn;n€Z