Question

Giải phương trình:

\(\dfrac{\sqrt{3}}{Cos^2x}+\dfrac{4+2Sin2x}{Sin2x}-2\sqrt{3}=2\left(Cotx+1\right)\)

Answer 1

ĐKXĐ: \(x\ne\dfrac{k\pi}{2}\)

\(\dfrac{\sqrt{3}}{cos^2x}+2+\dfrac{2}{sinx.cosx}-2\sqrt{3}=2\left(\dfrac{1}{tanx}+1\right)\)

\(\Leftrightarrow\sqrt{3}\left(1+tan^2x\right)+\dfrac{\dfrac{2}{cos^2x}}{\dfrac{sinx.cosx}{cos^2x}}+2-2\sqrt{3}=2\left(\dfrac{1}{tanx}+1\right)\)

\(\Leftrightarrow\sqrt{3}tan^2x+\dfrac{2\left(1+tan^2x\right)}{tanx}+2-\sqrt{3}=\dfrac{2}{tanx}+2\)

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

\(\Leftrightarrow\sqrt{3}tan^3x+2tan^2x-\sqrt{3}tanx=0\)

\(\Leftrightarrow...\)