Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\tan \dfrac{x}{2} = t \Rightarrow \dfrac{{\sin \dfrac{x}{2}}}{{\cos \dfrac{x}{2}}} = t \Leftrightarrow \sin \dfrac{x}{2} = t.\cos \dfrac{x}{2}\\
{\sin ^2}\dfrac{x}{2} + {\cos ^2}\dfrac{x}{2} = 1\\
\Leftrightarrow {\left( {t\cos \dfrac{x}{2}} \right)^2} + {\cos ^2}\dfrac{x}{2} = 1\\
\Leftrightarrow \left( {{t^2} + 1} \right).{\cos ^2}\dfrac{x}{2} = 1\\
\Leftrightarrow {\cos ^2}\dfrac{x}{2} = \dfrac{1}{{{t^2} + 1}}\\
\sin x = 2\sin \dfrac{x}{2}.\cos \dfrac{x}{2} = 2.t\cos \dfrac{x}{2}.\cos \dfrac{x}{2} = 2t.{\cos ^2}\dfrac{x}{2} = \dfrac{{2t}}{{{t^2} + 1}}\\
\cos x = 2{\cos ^2}\dfrac{x}{2} - 1 = \dfrac{2}{{{t^2} + 1}} - 1 = \dfrac{{2 - \left( {{t^2} + 1} \right)}}{{{t^2} + 1}} = \dfrac{{1 - {t^2}}}{{{t^2} + 1}}\\
\tan x = \dfrac{{\sin x}}{{\cos x}} = \dfrac{{2t}}{{1 - {t^2}}}
\end{array}\)
