Question

已知△的内角A，B，C的对边a b c，√3sinCcosC-cos^2C=1/2,且c=3 (1)求角C

(2)若向量m=(1,sinA)与n=(2,sinB）共线,求a,b的值

Answer 1

(1)
√3sinCcosC-cos^2C
=√3/2sin2C-1/2cos2C-1/2
=sin(2C-π/6)-1/2
=1/2
所以sin(2C-π/6)=1
那么2C-π/6=π/2
C=π/3
(2)
由题意
sinB=2sinA
则有sin(2/3π-A)=2sinA
-3/2sinA+√3/2cosA=0
所以tanA=√3/3
所以A=π/6
则B=π/2
那么应用正弦定理
sinA/a=sinB/b=sinC/c=(√3/2)/3
a=√3
b=2√3