\(\Leftrightarrow tan\left(pi+\dfrac{pi}{2}-x\right)+\dfrac{sinx}{1+cosx}=2\)
\(\Leftrightarrow cotx+\dfrac{sinx}{1+cosx}=2\)
\(\Leftrightarrow\dfrac{cosx}{sinx}+\dfrac{sinx}{1+cosx}=2\)
\(\Leftrightarrow\dfrac{cosx+cos^2x+sin^2x}{sinx\left(1+cosx\right)}=2\)
\(\Leftrightarrow sinx=\dfrac{1}{2}\)
=>x=pi/6+k2pi hoặc x=5/6pi+k2pi
ĐKXĐ: \(x\ne k\pi\)
\(tan\left(\dfrac{3\pi}{2}-x\right)+\dfrac{sinx}{1+cosx}=2\)
\(\Leftrightarrow cotx+\dfrac{sinx\left(1-cosx\right)}{\left(1-cosx\right)\left(1+cosx\right)}=2\)
\(\Leftrightarrow\dfrac{cosx}{sinx}+\dfrac{sinx\left(1-cosx\right)}{sin^2x}=2\)
\(\Leftrightarrow\dfrac{cosx}{sinx}+\dfrac{1-cosx}{sinx}=2\)
\(\Rightarrow1=2sinx\)
\(\Leftrightarrow sinx=\dfrac{1}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+k2\pi\\x=\dfrac{5\pi}{6}+k2\pi\end{matrix}\right.\)
