Chứng minh: sin6x*sin4x -sin15x*sin13x + in19x*sin9x=0

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Chứng minh: sin6x*sin4x -sin15x*sin13x + in19x*sin9x=0

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Claire 2 tuần 2021-08-28T07:05:09+00:00 1 Answers 4 views 0

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    2021-08-28T07:07:06+00:00

    Ta có:

     `\qquad sin6xsin4x-sin15xsin13x+sin19xsin9x`

    `=1/2[cos(6x-4x)-cos(6x+4x)]-1/2[cos(15x-13x)-cos(15x+13x)]+1/2[cos(19x-9x)-cos(19x+9x)]`

    `=1/2(cos2x-cos10x)-1/2(cos2x-cos28x)+1/2(cos10x-cos28x)`

    `=1/2cos2x-1/2cos10x-1/2cos2x+1/2cos28x+1/2cos10x-1/2cos28x`

    `=0`

    Vậy: `sin6xsin4x-sin15xsin13x+sin19xsin9x=0`

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