Question

高二数学化简 求过程

sinA*sin(120°-A)怎么化简

Answer 1

=sina(sin120cosa-sinacos120)
=sina(√3/2*cosa-sina/2)
=√3sin2a/4-sin²a/2
=√3sin2a/4-[(1-cos2a)/4]
=1/2*[√3sin2a/2-cos2a/2]-1/4
=1/2*[sin(2a-30)]
如果我说的那么详细你还不懂我就真的很生气咯！

追问

cos120不是=-1/2吗？

追答

很好，我故意化错，你检查出来咯

Answer 2

sinA*sin(120°-A)
=sinAsin(60+A)
设B=30+A
sin(B-30)sin(B+30)
=(sinB)^2-(sin30)^2
=(sin(A+30))^2-1/4
注：Sin(a-b)sin(a+b)=sin^a-sin^b 的证明
证:Sin(a-b)sin(a+b)=
(Sinacosb-cosasinb)*(Sinacosb+cosasinb)=
Sin^acos^b-cos^asin^b=
Sin^a(1-sin^b)-(1-sina^a)sin^b=
Sin^a-Sin^asin^b-sin^b+sina^asin^b=
sin^a-sin^b