证明sin(a+b)sin(a-b)=sin^2 a-sin^2 b,_数学解答

证明sin(a+b)sin(a-b)=sin^2 a-sin^2 b,

人气：164 ℃　时间：2020-05-14 08:12:21

解答

左边=(sinacosb+cosasinb)(sinacosb-cosasinb)
=sin²acos²b-cos²asin²b
=sin²a(1-sin²b)-(1-sin²a)sin²b
=sin²a-sin²asin²b-sin²b+sin²asin²b
=sin²a-sin²b
=右边
命题得证