已知sin(A+π/4)+sin(A-π/4)=根号2/3 1.求sinA的值 2.求【sin(A-π/4)】/【1-cos2A-_数学解答

已知sin(A+π/4)+sin(A-π/4)=根号2/3 1.求sinA的值 2.求【sin(A-π/4)】/【1-cos2A-sin2A】的值谢

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解答

(1)展开,得sinAcosπ/4 + cosAsinπ/4 + sinAcosπ/4 - cosAsinπ/4=2sinAcosπ/4=√2×sinA=√2/3
所以,sinA=1/3.
(2) 原式=[sinAcosπ/4 - cosAsinπ/4]/[2sin^A-2sinAcosA]=[√2/2]/2sinA=3√2/4.