Question

chứng minh rằng 1+ sinx+cosx+tanx= (1+ cosx)(1+tanx)

Answer 1

\(1+sinx+cosx+tanx=1+cosx+sinx+\frac{sinx}{cosx}\)

\(=1+cosx+\frac{sinx\left(1+cosx\right)}{cosx}=\left(1+cosx\right)\left(1+\frac{sinx}{cosx}\right)\)

\(=\left(1+cosx\right)\left(1+tanx\right)\)

Answer 2

\(VT=1+\cos x+\sin x+\dfrac{\sin x}{\cos x}\)       \(=1+\cos x+\dfrac{\sin x.\cos x+\sin x}{\cos x}\)       \(=1+\cos x+\dfrac{\sin x.\left(\cos x+1\right)}{\cos x}\)       \(=\left(1+\cos x\right)+\tan x.\left(1+\cos x\right)\)       \(=\left(1+\cos x\right)\left(1+\tan x\right)\)