Toán Lớp 11: Giải phương trình (tanx)/(1-tan^2x)=1/2cot(x+π/4)
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Toán Lớp 11: Giải phương trình (tanx)/(1-tan^2x)=1/2cot(x+π/4)
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\dfrac{{\tan x}}{{1 – {{\tan }^2}x}} = \dfrac{1}{2}\cot \left( {x + \dfrac{\pi }{4}} \right)\\
\Leftrightarrow \dfrac{{2\tan x}}{{1 – {{\tan }^2}x}} = \cot \left( {x + \dfrac{\pi }{4}} \right)\\
\Leftrightarrow \tan 2x = \cot \left( {x + \dfrac{\pi }{4}} \right)\\
\Leftrightarrow \cot \left( {\dfrac{\pi }{2} – 2x} \right) = \cot \left( {x + \dfrac{\pi }{4}} \right)\\
\Leftrightarrow x + \dfrac{\pi }{4} = \dfrac{\pi }{2} – 2x + k\pi \\
\Leftrightarrow 3x = \dfrac{\pi }{4} + k\pi \\
\Leftrightarrow x = \dfrac{\pi }{{12}} + \dfrac{{k\pi }}{3}\left( {k \in \mathbb{Z}} \right)
\end{array}$