作业帮10.11
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10.11
10.11
10.11
⒑sin(π/4＋α)=±√1－cos²(π/4＋α)=±(2√2)/3
∵0＜α＜π/2且cos(π/4＋α)＞0
∴sin(π/4＋α)=(2√2)/3
sin(π/4－β/2)=±√1－cos²(π/4－β/2)=±√6/3
∵-π/2＜β＜0
∴0＜-β＜π/2
∴0＜-β/2＜π/4
则π/4＜π/4－β/2＜π/2
∴sin(π/4－β/2)=√6/3
cos(α＋β/2)=cos[(π/4＋α)－(π/4－β/2)]=cos(π/4＋α)·cos(π/4－β/2)＋sin(π/4＋α)·sin(π/4－β/2)
=(1/3)×(√3/3)＋[(2√2)/3]×(√6/3)=5√3/9
选C
⒒m·n=√3sinA·cosB＋√3sinB·cosA=√3·sin(A＋B)=1＋cos(A＋B)
∵A、B、C是△ABC的3个内角
∴A＋B=π－C
∴√3sin(π－C)=1＋cos(π－C)
√3sinC=1－cosC
√3sinC＋cosC=1
2sin(C＋π/6)=1
sin(C＋π/6)=1/2
∴C=120°
选C