Question

1+ Tanx+tan^2x+tanx^3x=sinx+cosx/cos^3x giúp mình với

Answer 1

\(1+tanx+tan^2x+tan^3x\)

\(1+\dfrac{sinx}{cosx}+\dfrac{sin^2x}{cos^2x}+\dfrac{sin^3x}{cos^3x}\)

\(=\dfrac{cos^3x+sinx.cos^2x+sin^2x.cosx+sin^3x}{cos^3x}\)

\(=\dfrac{cos^2x.\left(sinx+cosx\right)+sin^2x.\left(sinx+cosx\right)}{cos^3x}\)

\(=\dfrac{\left(sin^2x+cos^2x\right)\left(sinx+cosx\right)}{cos^3x}=\dfrac{sinx+cosx}{cos^3x}\)

Answer 2

\(\dfrac{\sin x+\cos x}{\cos x}.\dfrac{1}{\cos^2x}=\left(\tan x+1\right)\left(\tan^2x+1\right)=\tan^4x+\tan x+\tan^2x+\left(đpcm\right)\)