Giải thích các bước giải:
Xét \(VT=\tan^{3} x+\tan^{2} x+\tan x+1\)
\(=\tan^{2} x(\tan x+1)+\tan x+1\)
\(=(\tan x+1)(\tan^{2} x+1)\)
\(=(\dfrac{\sin x}{\cos x}+1).\dfrac{1}{\cos^{2} x}\)
\(=\dfrac{\dfrac{\sin x+\cos x}{\cos x}}{\cos^{2} x}=\dfrac{\sin x+\cos x}{\cos^{3} x}=VP\)