$cos^2x - sin^2x =-(cos^5x - sin^5x)$
<->$ (cosx - sinx) (cosx + sinx) = -(cosx - sinx)( cos^4x + cos^3x sinx + cos^2x sin^2x + cosx sin^3x + sin^4x)$
<-> $cosx -sin x =0$ hoac $cosx + sinx = -(cos^4x + cos^3x sinx + cos^2x sin^2x + cosx sin^3x + sin^4x)$
TH1: $cosx - sinx = 0$
Vay $tanx = 1$ hay $x = \pi/2 + k\pi$.
TH2: $cosx + sinx = -(cos^4x + cos^3x sinx + cos^2x sin^2x + cosx sin^3x + sin^4x)$
<-> $cosx + sinx = -(cos^4x + sin^4x + cos^2x sin^2x + sinx cosx (sin^2x + cos^2x)$
<->$ cosx + sinx = -[(cos^2x + sin^2x)^2 - cos^2x sin^2x + sinx cosx$
<->$cosx + sinx = cos^2x sin^2x-1$
<->$ (cosx + sinx)^2 = (cos^2x sin^2x -1)^2$
<-> $ 1+2sinx cosx = sin^4x cos^4x -2sin^2x cos^2x + 1$
<-> $ sinx cosx (2-sin^3x cos^3x + 2sinx cosx) = 0$
<-> $sinx = 0$ hoac $cosx = 0$ hoac $2-sin^3x cos^3x + 2sinx cosx=0$
<-> $x = k\pi$ hoac $x = \pi/2 + k\pi$ hoac $sin^3x cos^3x - 2sinx cosx-2=0$
Xet ptrinh $sin^3x cos^3x - 2sinx cosx-2=0$
Dat $t = sinx cosx$ (ta co t = 1/2 sin 2x, vay $-1/2 \leq t \leq 1/2$)
Ptrinh tro thanh
$t^3 -2t-2=0$.
(Ban bam may giai ptrinh thi ptrinh vo nghiem nhe)
Vay $x = k \pi$ hoac $x = \pi/2 + k\pi$
