=2sin20+cos10+tan20sin10
=2sin20+cos10+sin20sin10/cos20
=[2sin20cos20+(cos10cos20+sin20sin10)]/cos20 (通分)
=[sin40+cos(20-10)]/cos20
=(sin40+sin80)/cos20
=(sin40+2sin40cos40)/cos20
=sin40(1+2cos40)/cos20
=2sin20(1+2cos40)
=2sin20(1+2sin50)
=2sin20(sin25*sin25+cos25*cos25+2sin25cos25)
=2sin20(sin25+cos25)*(sin25+cos25) 提一个根号2,再化为同一个角
=4sin20sin(25+45)
=4sin20sin70
=4sin20cos20
=2sin40