Question

\(4sin^3x+3sin^2x.cosx-sinx-cos^3x=0\)

Answer 1

Với \(cosx=0\) không phải nghiệm

Với \(cosx\ne0\) , chia 2 vế cho \(cos^3x\):

\(4tan^3x+3tan^2x-tanx.\left(1+tan^2x\right)-1=0\)

\(\Leftrightarrow3tan^3x+3tan^2x-tanx-1=0\)

\(\Leftrightarrow\left(tanx+1\right)\left(3tan^2x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}tanx=-1\\tanx=\dfrac{1}{\sqrt{3}}\\tanx=-\dfrac{1}{\sqrt{3}}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{4}+k\pi\\x=\pm\dfrac{\pi}{6}+k\pi\end{matrix}\right.\)