在三角形ABC中,给出下列4个式子1.sin(A+B)+sinC2.cos(A+B)+cosC3.sin(2A+2B)+sin2C4.cos(2A+2B)+cos2C为什么2和3为常数?常数是怎么定义的?

Question

在三角形ABC中,给出下列4个式子
1.sin(A+B)+sinC 2.cos(A+B)+cosC 3.sin(2A+2B)+sin2C 4.cos(2A+2B)+cos2C 为什么2和3为常数?常数是怎么定义的?

Answer 1

2.cos(A+B)+cosC
=cos(180-C)+cosC
=-cos(-C)+cosC
=-cosC+cosC
=0
3.sin(2A+2B)+sin2C
=sin(360-2C)+sin2c
=-sin2C+sin2C
=0
常数就是不含有未知数的项,比如2,比如3 答案补充 1.sin(A+B)+sinC =sin(180-c)+sinc=-sin(-c)+sinc=2sinc
4.cos(2A+2B)+cos2C=cos(360-2c)+cos2c=cos(-2c)+cos2c=2cos2c