分类：教育/科学-理工学科-数学
问题：紧急求助SIN69
SIN69-SIN3+SIN39-SIN33
回答：SIN69-SIN3+SIN39-SIN33

sin69°-sin3°+sin39°-sin33°
=(sin69°-sin33°)+(sin39°-sin3°)
=2cos51°sin18°+2cos21°sin18°
=2sin18°(cos51°+cos21°)
=2sin18°*(2cos36°cos15°)
=4sin18°*cos36°*cos15°
=2*(2*sin18°*cos18°)*cos36°*cos15°/cos18°
=2*sin36°*cos36°*cos15°/sin72°
=sin72°*cos15°/sin72°
=cos15°
=cos(45°-30°)
=cos45°cos30°+sin45°sin30°
=(√2/2)*(√3/2)+(√2/2)*(1/2)
=(√6+√2)/4