Question

sin6°+cos15°sin9°/cos6°-sin15°sin9° 详细解答过程

Answer 1

sin6°+cos15°sin9°
=sin(15-9)+cos15sin9
=sin15cos9-sin9cos15+cos15sin9
=sin15cos9

cos6°-sin15°sin9
=cos(15-9)-sin15sin9
=sin15sin9-cos15cos9-sin15sin9
=-cos15cos9

所以原式
=sin15/(-cos15)
=-tan15
=√3-2

追问

cos(15-9)不是等于cos15cos9+sin15sin9吗？

追答

O，对
cos6°-sin15°sin9
=cos(15-9)-sin15sin9
=sin15sin9+cos15cos9-sin15sin9
=cos15cos9

所以原式
=sin15/cos15
=tan15
=2-√3