Rút gọn : A = ( tan3x + tanx ) ( tan3x – tanx )

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1. Đáp án:

    

   Giải thích các bước giải:

   $ (tan3x + tanx)(tan3x – tanx)$

   $ = (\dfrac{sin3x}{cos3x} + \dfrac{sinx}{cosx})(\dfrac{sin3x}{cos3x} – \dfrac{sinx}{cosx})$

   $ = (\dfrac{sin3xcosx + cos3xsinx}{cosxcos3x}).(\dfrac{sin3xcosx – cos3xsinx}{cosxcos3x})$

   $ = \dfrac{sin(3x + x)}{cosxcos3x}.\dfrac{sin(3x – x)}{cosxcos3x}$

   $ = \dfrac{sin4xsin2x}{cos²xcos²3x} = \dfrac{2cos2xsin²2x}{cos²xcos²3x}$

   $ = \dfrac{8cos2xsin²xcos²x}{cos²xcos²3x} = \dfrac{8cos2xcos²x}{cos²3x}.$

    

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