$1.tanx + cotx=-2\sqrt{2}$$<=> 1/sinx*cosx=-2\sqrt{2}$$<=> sin2x=-1/\sqrt{2}$$<=>x= -\Pi/8 + k\Pi$ hc $x=5\Pi/8 + k\Pi$2.$sinx + cosx =\sqrt{2}$<=>$ \sqrt{2}sin(x+\Pi/4)=\sqrt{2}$3. sin^6 + cos^6=7/16sin^6 + cos^6 = (sin^2+cos^2)*(sin^4 + cos^4 -sin^2*cos^2)=sin^4 + cos^4 - sin^2*cos^2=(sin^2 + cos^2)^2 -3sin^2*cos^2=1-3/4sin^2(2x)=5/8 - cos4x=> cos 4x=3/16
$1.tanx + cotx=-2\sqrt{2}$$
\Left
rig
ht
arrow \frac1
{sinx
.cosx
}=-2\sqrt{2}$$
\Left
rig
ht
arrow sin2x=
\frac{-1
}{\sqrt{2}
}$$
\Left
rig
ht
arrow x= -\
frac{\pi
}8 + k\
pi$ hc $x=
\frac{5\
pi
}8 + k\
pi$2.$sinx + cosx =\sqrt{2}$
$\Left
rig
ht
arrow \sqrt{2}sin(x+\
frac{\pi
}4)=\sqrt{2}$3.
$sin^6 + cos^6=
\frac7
{16
}$$sin^6 + cos^6 = (sin^2+cos^2)(sin^4 + cos^4 -sin^2
.cos^2)=sin^4 + cos^4 - sin^2
.cos^2
$$=(sin^2 + cos^2)^2 -3sin^2
.cos^2=1-
\frac3
{4
}sin^2(2x)=
\frac5
{8
} - cos4x
\Rig
ht
arrow cos 4x=
\frac3
{16
}$