已知：sin(α+π/3)+sinα=负2分之根号3 α∈（-π/2,0）求cosα_数学解答

已知：sin(α+π/3)+sinα=负2分之根号3 α∈（-π/2,0）求cosα

人气：283 ℃　时间：2020-01-29 05:45:31

解答

sin(α+π/3)+sinα
=[sina/2+√3cosa/2]+sina
=3sina/2+√3cosa/2
=√3[√3sina/2+cosa/2]
=√3sin(a+π/6)=-√3/2
sin(a+π/6)=-1/2
a=-π/3
cosa=cos(π/3)=1/2