Question

sin² x (tan x +1)= 3 sin x (cos x - sin x) +3

Answer 1

ĐKXĐ : \(x\ne\dfrac{\pi}{2}+k\pi\left(k\in Z\right)\)

... \(\Leftrightarrow\)\(sin^2x\left(tanx+1\right)=3\left[sinx.cosx-sin^2x+sin^2x+cos^2x\right]\)

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

\(\Leftrightarrow\left(sinx+cosx\right)\left[\dfrac{sin^2x}{cosx}-3cosx\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sinx+cosx=0\left(1\right)\\sin^2x=3cos^2x\left(2\right)\end{matrix}\right.\)

(1) \(\Leftrightarrow\sqrt{2}sin\left(x+\dfrac{\pi}{4}\right)=0\) \(\Leftrightarrow...\)

(2) \(\Leftrightarrow1=4cos^2x\Leftrightarrow...\)