求值：cos40°(1+3tan10°)=_．
问题描述：
求值：cos40°(1+
tan10°)=______．
3
答
cos40°(1+
tan10°)=sin50°(1+
3
tan10°)=
3
=sin50°(cos10°+
sin10°)
3
cos10°
=2sin50°sin(30°+10°) cos10°
=2cos40° sin40° cos10°
=1sin80° cos10°
故答案为：1．