求cos(80°+2α)cos(65°+2α)+sin(80°+2α)sin(65°+2α)的值
题目
求cos(80°+2α)cos(65°+2α)+sin(80°+2α)sin(65°+2α)的值
答案
cos(80°+2α)cos(65°+2α)+sin(80°+2α)sin(65°+2α)
=cos[(80°+2α)-(65°+2α)]
=cos15°
=cos(45°-30°)
=cos45°cos30°+sin45°sin15°
=(√6+√2)/4
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