不查表求值:cos40°•cos80°+cos80°•cos160°+cos160°•cos40°.
解:原式=
![](http://thumb.1010pic.com/pic5/latex/13.png)
[cos120°+cos(-40°)+cos240°+cos(-80°)+cos200°+cos120°]
=
![](http://thumb.1010pic.com/pic5/latex/13.png)
(-cos60°+cos40°-cos60°+cos80°-cos20°-cos60°)
=
![](http://thumb.1010pic.com/pic5/latex/13.png)
[-
![](http://thumb.1010pic.com/pic5/latex/33.png)
+cos(60°-20°)+cos(60°+20°)-cos20°]
=
![](http://thumb.1010pic.com/pic5/latex/13.png)
[-
![](http://thumb.1010pic.com/pic5/latex/33.png)
+cos60°cos20°+sin60°sin20°+cos60°cos20°-sin60°sin20°-cos20°]
=
![](http://thumb.1010pic.com/pic5/latex/13.png)
[-
![](http://thumb.1010pic.com/pic5/latex/33.png)
+cos20°-cos20°]
=-
![](http://thumb.1010pic.com/pic5/latex/365.png)
分析:把原式的三个加数利用积化和差公式和诱导公式化简后,将40°变为60°-20°,80°变为60°+20°,然后利用两角和与差的余弦函数公式及特殊角的三角函数公式化简后,即可求出值.
点评:此题考查学生灵活运用积化和差公式及诱导公式化简求值,灵活运用两角和与差的余弦函数公式化简求值,是一道中档题.学生做题时注意将40°变为60°-20°,80°变为60°+20°.