Chứng minh rằng: $\dfrac{cos4x+cos2x}{sin4x-sin2x}=cotx$

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Chứng minh rằng: $\dfrac{cos4x+cos2x}{sin4x-sin2x}=cotx$

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Gabriella 3 tháng 2021-09-10T03:09:44+00:00 1 Answers 10 views 0

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    2021-09-10T03:11:33+00:00

    Giải thích các bước giải:

    $\begin{array}{l}
    \dfrac{{\cos 4x + \cos 2x}}{{\sin 4x – \sin 2x}}\\
     = \dfrac{{2{{\cos }^2}2x + \cos 2x – 1}}{{\sin 2x\left( {2\cos 2x – 1} \right)}}\\
     = \dfrac{{\left( {2\cos 2x – 1} \right)\left( {\cos 2x + 1} \right)}}{{\sin 2x\left( {2\cos 2x – 1} \right)}}\\
     = \dfrac{{\cos 2x + 1}}{{\sin 2x}}\\
     = \dfrac{{2{{\cos }^2}x}}{{2\sin x\cos x}}\\
     = \dfrac{{\cos x}}{{\sin x}}\\
     = \cot x
    \end{array}$

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