Question

已知sinA=1/√5,sinB=1/√10,且A，B为锐角，

已知sinA=1/√5,sinB=1/√10,且A，B为锐角，
求A+B的值

Answer 1

∵sinA=1/√5＜1/√2=sin45°，∴0＜A＜45°，∴cosA=2√5
∵sinB=1/√10＜1/√2=sin45°，∴0＜B＜45°，∴cosB=3/√10
∴0＜A+B＜90°
∴sin(A+B)=sinAcosB+cosAsinB=1/√2
∴A+B=45°

Answer 2

由题意知
cosA=2/√5,cosB=3/√10
sin(A+B)=sinAcosB+cosAsinB=1/√5
A+B=arcsin(1/√5)

Answer 3

首先求出sin(A+B)的值，好像有个公式来着 可以套出来

Answer 4

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