Question

已知根号3sina_sin(π/2_2a)/cos(π+a).cosa=1.a∈(0,π).求a的值

Answer 1

√3sina-sin(π/2-2a)/cos(π+a).cosa=1
√3sina-cos2a/(-cosa)*cosa=1
√3sina+cos2a-1=0
√3sina-2sin^2a=0
(√3-2sina)sina=0
sina=0或sina= √3/2

a=π/3

追问

还有3π/2,sin120=根号3/2

追答

a=π/3 ,a=2π/3

Answer 2

sina-sinb=-1/2 sin a-2sinasinb+sin b=1/4(1) cosa-cosb=√3/2又因为sina-sinb=-1/2<0 所以a<b a-b<0 那么a-b=-π/3