利用特殊角的三角函数值计算cos15°cos105°-sin105°sin15°sin20°sin10°-cos10°sin70°

问题描述:

利用特殊角的三角函数值计算
cos15°cos105°-sin105°sin15°
sin20°sin10°-cos10°sin70°

cos15°cos105°-sin105°sin15°
=cos(105°+15°)
=cos(120°)
=1/2
sin20°sin10°-cos10°sin70°
=cos70°sin10°-cos10°sin70°
=sin(10°-70°)
=sin(-60°)
=-sin(60°)
=-√3/2

cos15°cos105°-sin105°sin15°
=cos(105°-15°)
=cos(90°)
=0
sin20°sin10°-cos10°sin70°
=cos70°sin10°-cos10°sin70°
=sin(10°-70°)
=sin(-60°)
=-cos(30°)
=-√3/2