2sin^2 alpha- 3sin alpha -2 =0 tinh tan alpha

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1. Đáp án:

   $\begin{array}{l}
   2{\sin ^2}a – 3\sin a – 2 = 0\\
    \Rightarrow 2.{\sin ^2}a – 4\sin a + \sin a – 2 = 0\\
    \Rightarrow 2\sin a\left( {{\mathop{\rm sina}\nolimits}  – 2} \right) + \left( {\sin a – 2} \right) = 0\\
    \Rightarrow \left( {\sin a – 2} \right)\left( {2\sin a + 1} \right) = 0\\
    \Rightarrow \sin a =  – \dfrac{1}{2}\left( {do: – 1 \le \sin a \le 1} \right)\\
   Do:{\sin ^2}a + {\cos ^2}a = 1\\
    \Rightarrow {\cos ^2}a = 1 – \dfrac{1}{4} = \dfrac{3}{4}\\
   \dfrac{1}{{{{\cos }^2}a}} = {\tan ^2}a + 1\\
    \Rightarrow {\tan ^2}a = \dfrac{1}{{{{\cos }^2}a}} – 1 = \dfrac{1}{3}\\
    \Rightarrow \left[ \begin{array}{l}
   \tan a = \dfrac{{\sqrt 3 }}{3}\\
   \tan a =  – \dfrac{{\sqrt 3 }}{3}
   \end{array} \right.
   \end{array}$

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2. $2\sin^2\alpha-3\sin\alpha-2=0$

   $\Leftrightarrow (\sin \alpha-2)(2\sin\alpha+1)=0$

   $\Leftrightarrow \sin \alpha=\dfrac{-1}{2}$

   $\dfrac{1}{\sin^2\alpha}=1+\cot^2\alpha$

   $\Rightarrow \cot^2\alpha=3$

   $\Leftrightarrow \tan^2\alpha=\dfrac{1}{3}$

   $\Leftrightarrow \tan \alpha=\pm\dfrac{1}{\sqrt3}$

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