Chứng minh: (1+cos x)/sin x – sin x/(1+cos x) = 2cot x

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Chứng minh: (1+cos x)/sin x – sin x/(1+cos x) = 2cot x

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Amity 3 years 2021-04-19T05:10:11+00:00 1 Answers 10 views 0

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  1. Ladonna
    0
    2021-04-19T05:11:47+00:00
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    $VT=\dfrac{1+\cos x}{\sin x}-\dfrac{\sin x}{1+\cos x}$

    $=\dfrac{(1+\cos x)^2-\sin^2x}{\sin x(1+\cos x)}$

    $=\dfrac{1+2\cos x+\cos^2x-\sin^2x}{\sin x(1+\cos x)}$

    $=\dfrac{2\cos x+2\cos^2x}{\sin x(1+\cos x)}$

    $=\dfrac{2\cos x(1+\cos x)}{\sin x(1+\cos x)}$

    $=\dfrac{2\cos x}{\sin x}$

    $=2\cot x$

    $=VP$

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