Tính tan10.tan25+tan25.tan55+tan55.tan10

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1. Đáp án:

    $1$

   Giải thích các bước giải: 

   `\qquad tan10°.tan25°+tan25°.tan55°+tan55°.tan10°`

   `=tan10°. (tan55°+tan25°)+tan55°.tan25°`

   `=tan10°. ({sin55°}/{cos55°}+{sin25°}/{cos25°})+{sin55°}/{cos55°}.{sin25°}/{cos25°}`

   `=cot80°. {sin55°cos25°+cos55°sin25°}/{cos55°cos25°}+{1/ 2 .  [cos(55°-25°)-cos(55°+25°)]}/{cos55°cos25°}`

   `={cos80°}/{sin80°} . {sin80°}/{cos55°.cos25°}+1/ 2 . {cos30°-cos80°}/{cos55°.cos25°}`

   `={cos80°}/{cos55°.cos25°}+1/ 2 . {cos30°-cos80°}/{cos55°.cos25°}`

   `={2cos80°+cos30°-cos80°}/{2cos55°.cos25°}`

   `={cos80°+cos30°}/{2. 1/ 2 .[cos(55°+25°)+cos(55°-25°)]}`

   `={cos80°+cos30°}/{cos80°+cos30°}=1`

   Vậy `tan10°.tan25°+tan25°.tan55°+tan55°.tan10°=1`

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