问题
解答题
已知函数f(x)=
(1)求a与ω的值; (2)在△ABC中,a,b,c分别是角A,B,C的对边,且f(A)=2,求
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答案
(1)f(x)=
asinωx-acosωx=2asin(ωx-3
)π 6
由已知周期T=
-4π 3
=π,故a=1,ω=2;π 3
(2)由f(A)=2,即sin(2A-
)=1,又-π 6
<2A-π 6
<π 6
,11π 6
则2A-
=π 6
,解得A═60°π 2
故
=b-2c acos(60°+c)
=sinB-2sinC sinAcos(60°+c) sin(120°-C)-2sinC sin60°cos(60°+C)
=
=
cosC+3 2
sinC-2sinC1 2
(3 2
cosC-1 2
sinC)3 2
=2.
cosC-3 2
sinC3 2
(1 2
cosC-3 2
sinC)3 2