求cos(80°+2α)cos(65°+2α)+sin(80°+2α)sin(65°+2α)的值

问题描述:

求cos(80°+2α)cos(65°+2α)+sin(80°+2α)sin(65°+2α)的值

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