Question

(cot20°-√3)(cos5°+sin5°)(cos5°-sin5°)

Answer 1

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