Biểu thức không phụ thuộc vào biến $x\Leftrightarrow$ biểu thức bằng một hằng số.
$A=(\cot x+\tan x)^2-(\cot x-\tan x)^2$
$=(\cot x+\tan x-\cot x+\tan x)(\cot x+\tan x +\cot x-\tan x)$
$=2\tan x.2\cot x$
$=2.2=4$
$B=3(\sin^4x+\cos^4x)-2(\sin^6x+\cos^6x)$
$=3(\sin^4x+\cos^4x)-2(\sin^2x+\cos^2x)(\sin^4x+\cos^4x-\sin^2x\cos^2x)$
$=3\sin^4x+3\cos^4x-2[(\sin^2x+\cos^2x)^2-2\sin^2x\cos^2x-\sin^2x\cos^2x)$
$=3\sin^4x+3\cos^4x-2(1-3\sin^2x\cos^2x)$
$=3(\sin^4x+2\sin^2x\cos^2x+\cos^4x)^2-2$
$=3(\sin^2x+\cos^2x)^2-2$
$=3-2=1$
$C=(a\tan x-b\cot x)^2-(a\tan x+b\cot x)^2$
$=(a\tan x-b\cot x-a\tan x-b\cot x)(a\tan x-b\cot x+a\tan x+b\cot x)$
$=-2a\tan x.2b\cot x$
$=-4ab$
$D=2\cos^4x-\sin^4x+\sin^2x\cos^2x+3\sin^2x$
$=\cos^4x-\sin^4x+\cos^4x+\sin^2x\cos^2x+3\sin^2x$
$=(\cos^2x-\sin^2x)(\cos^2x+\sin^2x)+\cos^4x+\sin^2x\cos^2x+3\sin^2x$
$=\cos^2x-\sin^2x+\cos^4x+\sin^2x\cos^2x+3\sin^2x$
$=1-2\sin^2x+3\sin^2x+\cos^4x+\sin^2x\cos^2x$
$=1+\sin^2x+\cos^4x+\sin^2x\cos^2x$
$=\cos^2x(\sin^2x+\cos^2x)+\sin^2x+1$
$=\cos^2x+\sin^2x+1=2$