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紧急求助SIN69
发表于：2024-10-24 00:00:00浏览：7次
问题描述：SIN69-SIN3+SIN39-SIN33
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
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