Toán Lớp 11: Rút gọn biểu thức A=sin2a+sin3a+sin4a/cos2a+cos3a+cos4a
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Toán Lớp 11: Rút gọn biểu thức A=sin2a+sin3a+sin4a/cos2a+cos3a+cos4a
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\dfrac{{\sin 2a + \sin 3a + \sin 4a}}{{\cos 2a + \cos 3a + \cos 4a}}\\
= \dfrac{{\left( {\sin 2a + \sin 4a} \right) + \sin 3a}}{{\left( {\cos 2a + \cos 4a} \right) + \cos 3a}}\\
= \dfrac{{2\sin 3a\cos a + \sin 3a}}{{2\cos 3a\cos a + \cos 3a}} = \dfrac{{\sin 3a\left( {2\cos a + 1} \right)}}{{\cos 3a\left( {2\cos a + 1} \right)}}\\
= \dfrac{{\sin 3a}}{{\cos 3a}} = \tan 3a
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