a向量=（根号3cosx/2,2cosx/2）,向量b=（2cosx/2,-sinx/2）函数f（x）=向量a·向量b

题目

a向量=（根号3cosx/2,2cosx/2）,向量b=（2cosx/2,-sinx/2）函数f（x）=向量a·向量b
1）设θ∈[-π/2,π/2],且f（θ）=根号3 +1,求θ的值
2）在△ABC中,AB=1,f（C）=根号3 +1,且△ABC的面积为 根号3 /2,求sinA+sinB的值

答案

(1)
f(x) = a.b
=（√3cosx/2,2cosx/2）.（2cosx/2,-sinx/2）
= 2√3(cosx/2)^2 - sinx
f（θ）=√3 +1
√3 +1 = 2√3(cosθ/2)^2 - sinθ
= √3( cosθ +1) - sinθ
1= √3cosθ - sinθ
1/2= (√3/2)cosθ - (1/2)sinθ
= sin(π/3+θ)
π/3+θ = π/6
θ = -π/6
(2) To be continued. .