Question

1.不查表,求下列各式的值：（1）cos75°；（2)cos(-65/12π）；(3)cos100°cos20°-sin

Answer 1

(1)75`=30`+45`,用和角公式展开.

(2)-65/12π=-6π+7/12π

7/12π＝π/3+π/4,用和角公式展开.

（3）cos100°cos20°-sin100°sin20°＝cos(100`+20`)=cos120`=-cos60`=-1/2

(4)cos63°cos33°+sin63°cos57°=cos63°cos33°+sin63°sin33°=cos(63`-33`)=cos30`=√3/2

2、cos105°cos45°+sin105°sin45°=cos(105`-45`)=cos60`=1/2

B