CM: tan^3 x +tan^2 x +tan x +1+=(sin x +cos x)/cos^3 x help me and i will vote 5 star for you !!! 10/08/2021 Bởi Melody CM: tan^3 x +tan^2 x +tan x +1+=(sin x +cos x)/cos^3 x help me and i will vote 5 star for you !!!
Giải thích các bước giải: Xét \(VT=\tan^{3} x+\tan^{2} x+\tan x+1\) \(=\tan^{2} x(\tan x+1)+\tan x+1\) \(=(\tan x+1)(\tan^{2} x+1)\) \(=(\dfrac{\sin x}{\cos x}+1).\dfrac{1}{\cos^{2} x}\) \(=\dfrac{\dfrac{\sin x+\cos x}{\cos x}}{\cos^{2} x}=\dfrac{\sin x+\cos x}{\cos^{3} x}=VP\) Bình luận
Giải thích các bước giải:
Xét \(VT=\tan^{3} x+\tan^{2} x+\tan x+1\)
\(=\tan^{2} x(\tan x+1)+\tan x+1\)
\(=(\tan x+1)(\tan^{2} x+1)\)
\(=(\dfrac{\sin x}{\cos x}+1).\dfrac{1}{\cos^{2} x}\)
\(=\dfrac{\dfrac{\sin x+\cos x}{\cos x}}{\cos^{2} x}=\dfrac{\sin x+\cos x}{\cos^{3} x}=VP\)
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