在△ABC中,角A,B,C所对的边分别为a,b,c,且满足csinA=3acosC.(1)求角C的大小;(2)求3sinA?sin

2025-04-02 07:57:16
推荐回答(1个)
回答1:

(1)由csinA=

3
acosC,结合正弦定理得,
a
sinA
=
c
3
cosC
=
c
sinC

∴sinC=
3
cosC,即tanC=
3

∵0<C<π,∴C=
π
3

(2)由(1)知B=
3
-A,
3
sinA-sin(B+
π
2
)=
3
sinA-cosB=
3
sinA-cos(