Chứng minh rằng cos4x + sin4x.tan2x – $2sin^{2}x$ = cos2x

Question

Chứng minh rằng
cos4x + sin4x.tan2x – $2sin^{2}x$ = cos2x

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Adalyn 2 tháng 2021-10-13T02:28:07+00:00 2 Answers 4 views 0

Answers ( )

    0
    2021-10-13T02:29:14+00:00

    Ta có

    $VT = \cos(4x) + \sin(4x) \tan(2x) – 2\sin^2x$

    $= 2\cos^2(2x) – 1 + 2\sin(2x) \cos(2x) . \dfrac{\sin(2x)}{\cos(2x)} – [1 – \cos(2x)]$

    $= 2\cos^2(2x) – 1 + 2\sin^2(2x) – 1 + \cos(2x)$

    $= 2[\cos^2(2x) + \sin^2(2x)] – 2 + \cos(2)$

    $= 2.1 – 2 + \cos(2x)$

    $= \cos(2x) = VP$

    0
    2021-10-13T02:30:02+00:00

    Đáp án:

     

    Giải thích các bước giải:

    $ cos4x + sin4x.tan2x – 2sin²x = (1 – 2sin²2x) + 2sin²2x – 2sin²x = cos2x$

     

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