Giải các phương trình :
$1. (1+tanx)cos^{3}x+(1+cotx)sin^3x=\sqrt{2 sin2x}$
$2. \frac{1}{1+cos2x}+\frac{1}{1+cos4x}+\frac{1}{1-cos6x}=2$
$3. 4(2cos^22x+cos2x-1)-6(cos2x-2sin^23x)-tanx=27$
$4. (cos2x-cos4x)^2=6+2sin3x$
$5. \frac{sin^3x.sin3x +cos^3x.cos3x}{tan(x-\frac{pi}{6}).tan(x+\frac{pi}{3})}=\frac{-1}{8}$
$6. 3tan2x-\frac{3}{cos2x}-2.\frac{1-cotx}{1+cotx}+2cos2x = 0$
$7. \frac{cos^42x+sin^42x}{tan(\frac{pi}{4}-x).tan(\frac{pi}{4}+x)}=cos^44x$
$8. sinx(1+tanx.tan\frac{x}{2})+tanx+2\sqrt{3}=\frac{\sqrt{3}}{cos^2x}$
