求 2sin160-cos170-tan160sin170 的值.其中的160 170 为度数,不是弧度,2 为系数

思路：首先已知中角度过大，用诱导公式先将角度化小；再根据情况组合进行积化和差，和差化积。最终达到化简求值的目的
2sin160`-cos170`-tan160`sin170 =2sin20+cos10+tg20sin10
=sin20+cos10+[sin20+tg20sin10] (将2sin20分成sin20+sin20)
=sin20+sin80+sin20[1＋sin10/cos20] (组合分配) =2sin50cos30+sin20/cos20[cos20+cos80] (和差化积,通分) = 2sin50cos30+sin20/cos20[2cos50.cos30] =2cos30[sin50+sin20cos50/cos20] =2cos30[sin50cos20+cos50sin20]/cos20 (积化和差) =2cos30sin70/cos20 =2cos30 =√3

原式=2sin20+cos10+sin10sin20/cos20
=2sin20+(cos10cos20+sin10sin20)/cos20
=2sin20+cos10/cos20
=(sin40+sin80)/cos20
=2sin60cos20/cos20
=√3