1)cos4x-cos^2x=1 2)sinx+cosx=-1

Question

1)cos4x-cos^2x=1
2)sinx+cosx=-1

Answer 1

1
2cos²2x-1-(1+cos2x)/2=1
4cos²2x-2-1-cos2x-2=0
cos2x=a
4a²-a-5=0
D=1+80=81
a1=(1-9)/8=-1⇒cos2x=-1⇒2x=π+2πn⇒x=π/2+πn,n∈z
a2=(1+9)/8=5/4⇒cos2x=5/4>1 нет решения