1+cos20度/2sin20度-sin10度(cot5度-tan5度)

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  • (1+cos20°)/2sin20°-sin10°(cot5°-tan5°)

    =(1+cos20°)/4sin10°cos10°-sin10°(cot5°-tan5°)

    =2cos10°/4sin10°-2sin5°cos5°(cot5°-tan5°)

    =cos10°/2sin10°-2((cos5°) ^2 -(sin5°)^2)

    =cos10°/2sin10°-2cos10°

    =(cos10°-4sin10°cos10°)/2sin10°

    =(sin80°-2sin20°)/2sin10°

    =((sin80°-sin20°)-sin20°)/2sin10°

    =(2cos50°sin30°-sin20°)/2sin10°

    =(sin40°-sin20°)/2sin10°

    =2cos30°sin10°/2sin10°

    =cos30°

    =√3/2