求 2sin160°-cos170°-tan160°sin170° 的值
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/17 05:38:10
求 2sin160°-cos170°-tan160°sin170° 的值
求 2sin160°-cos170°-tan160°sin170° 的值
求 2sin160°-cos170°-tan160°sin170° 的值
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
=(2sin20cos20+cos10)/cos20
=(sin40+sin80)/cos20
=[sin(60-20)+sin(60+20)]/cos20
=(sin60cos20-cos60sin20+sin60cos20+cos60sin20)/cos20
=2sin60cos20/cos20
2sin60
=√3
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=2sin20°+cos10°+tan20°sin10°
=(2sin20°cos20°+cos10°cos20°+sin20°sin10°)/cos20°
=(sin40°+cos10°)/cos20°
=(cos50°+cos10°)/cos20°
=(cos30°cos20°)/cos20°
=cos30°
=√3/2