化简：sin48°×sin57°—sin42°sin33°
问题描述：
化简：sin48°×sin57°—sin42°sin33°
答
第一个方法∶
sin48°×sin57°-sin42°sin33°
=sin48°×cos33°-cos48°sin33°
=sin(48-33)°
=sin15°
=sin(60-45)°
=sin60°×cos45°-cos60°sin45°
=√3/2×√2/2-1/2×√2/2
=(√6-√2)/4
第二个方法∶
cos42°×cos33°-sin42°sin33°
=cos(42+33)°
=cos75°
=cos(45°+30°)
=cos45°×cos30°-sin45°sin30°
=√2/2×√3/2-√2/2×1/2
=(√6-√2)/4