化简[2sin50°+sin10°(1+3tan10°)]1+cos20°．
问题描述：
化简[2sin50°+sin10°(1+
tan10°)]
3
．
1+cos20°
答
原式=[2sin50°+sin10°（1+
）]
sin10°
3
cos10°
1+cos20°
=（2sin50°+sin10°•
）cos10°+
sin10°
3
cos10°
1+cos20°
=（2sin50°+2sin10°•
）sin(10°+30°) cos10°
1+cos20°
=
•2sin50°cos10°+2sin10°sin40° cos10°
1+cos20°
=2cos（40°-10°）•
cos10°
2
cos10°
=2cos30°×
2
=
．
6