cos100°-cos40°=（-sin70°）怎么从左边推算到右边的?

题目

cos100°-cos40°=（-sin70°）怎么从左边推算到右边的?

答案

cos100°-cos40°
=cos(70°+30°)-cos(70°-30°)
=cos70°cos30°-sin70°sin30°-cos70°cos30°-sin70°sin30°
=-2sin30°sin70°
=-2*(1/2)*sin70°
=-sin70°