Question

化简1+sin40°-cos40°/1+sin40°+cos40°

Answer 1

=1+2sin20°cos20°-（1-2sin²20°）/1+2sin20°cos20°+（2cos²20°-1）
=2sin20°cos20°+2sin²20°/2sin20°cos20°+2cos²20°
=2sin20°（cos20°+sin20°）/2cos20°（sin20°+cos20°）
=2sin20°/2cos20°
=tan20°

自己蒙的，不知对不对

Answer 2

( 1 + cos40 )/ sin40 = sin40 /( 1 - cos40 ) = (1 + sin40�+ cos40 )/( 1 + sin40 -cos40 )

( 1 + cos40 )/ sin40 = 2(cos20)^2 / (2sin20cos20) = cot20

所以原式=cot20

Answer 3

1+sin40-cos40
=1+2sin20cos20-(1-2sin²20)
=2sin20cos20+2sin²20
=2sin20(sin20+cos20)

1+sin40+cos40
=1+2sin20cos20+2cos²20-1
=2cos20(sin20+cos20)

(1+sin40-cos40)/(1+sin40+cos40)
=2sin20(sin20+cos20)/2cos20(sin20+cos20)
=tan20

Answer 4

1+sin40°-cos40°/1+sin40°+cos40°
=(2sin^220°+2sin20°cos20°)/(2sin20°cos20°+2cos^2 20°)
=2sin20°(sin20°+cos20°)/2cos20°(sin20°+cos20°)
=tan20°