求 2sin160°-cos170°-tan160°sin170° 的值

原式=2sin20°+cos10°+tan20°sin10°
=(2sin20°cos20°+cos10°cos20°+sin20°sin10°)/cos20°
=(sin40°+cos10°)/cos20°
=(cos50°+cos10°)/cos20°
=(cos30°cos20°)/cos20°
=cos30°
=√3/2

原式用诱导公式并切化弦得:2sin20+cos10+sin20*sin10/cos20
=(2sin20cos20+cos20cos10+sin20sin10)/cos20
=(sin40+sin80)/cos20
=2sin60cos20/cos20(和差化积)
=根号3

原式=2sin(180-20)-cos(180-10)-tan(180-20)sin(180-10)=2sin20+cos10+tan20sin10=2sin20+cos10+(sin20/cos20)sin10=2sin20+cos10+sin10sin20/cos20=2sin20+(cos20cos10+sin10sin20)/cos20=2sin20+cos(20-10)/cos20=...