tan9°-tan27°-tan63°+tan81=?(不用和差化积)

发布网友 发布时间：2024-10-23 21:50

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热心网友 时间：2024-10-26 06:30

tan9°-tan27°-tan63°+tan81 =
tg9 + ctg9 - (tg27 + ctg27 ) =
sin9/cos9 + cos9/sin9 - (sin27/cos27 + cos27/sin27) =
1/(sin9cos9) - 1/(sin27cos27) =
2 * [1/sin18 - 1/sin54] =
2 * [1/sin18 - 1/cos36] =
2 * [2cos18/sin36 - 1/cos36] =
2 * [(2cos18cos36 - sin36)/sin36cos36] =
2 * [(2cos18cos36 - cos54)/sin36cos36] =
2 * [(2cos18cos36 - cos18cos26 + sin18sin36)/sin36cos36] =
2 * [(cos18cos36 + sin18sin36)/sin36cos36] =
2 * [cos18/sin36cos36] =
2 * [sin72 / (1/2 * sin72)] =
4

用到了和角公式，不知算不算和差化积.

热心网友 时间：2024-10-26 06:27

用tan(a)+tan(b)=tan(a+b)[1-tan(a)*tan(b)]试试，我就不做了