(cot20°-√3)(cos5°+sin5°)(cos5°-sin5°)计算
问题描述：
(cot20°-√3)(cos5°+sin5°)(cos5°-sin5°)计算
答
原式=(cos20/sin20-√3)(cos²5-sin²5)
=(cos20/2sin10cos10-√3)cos10
=cos20/(2sin10)-√3cos10
=(cos20-2√3sin10cos10)/(2sin10)
=(cos20-√3sin20)/(2sin10)
=2(cos20*1/2-sin20*√3/2)/(2sin10)
=(cos20cos60-sin20sin60)/sin10
=cos(20+60)/sin10
=cos80/sin10
=sin10/sin10
=1