Question

sinA+sin（2π/3-A）A∈（0，2π/3）求值域

Answer 1

原式=sinA + sin(2π/3)cosA - cos(2π/3)sinA
=sinA + (√3/2)cosA + (1/2)sinA
=(3/2)sinA + (√3/2)cosA
=√3·[(√3/2)sinA + (1/2)cosA]
=√3·sin(A + π/6)
∵0＜A＜2π/3
∴π/6＜A + π/6＜5π/6
则1/2＜sin(A + π/6)≤1
∴值域是(√3/2，√3]

Answer 2

套和差化积
=2sinπ/3cos(A－π/3)
=√3cos(A－π/3)
A∈(0.2π/3)
A－π/3∈(－π/3.π/3)
cos(A－π/3)∈(1/2.1)
值域∈(√3/2.√3)

Answer 3

和差化积，值域为(-1/2，1)。

Answer 4

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