来自唐伦的问题
【已知sin(A+π/4)+sin(A-π/4)=根号2/31.求sinA的值2.求【sin(A-π/4)】/【1-cos2A-sin2A】的值谢】
已知sin(A+π/4)+sin(A-π/4)=根号2/31.求sinA的值2.求【sin(A-π/4)】/【1-cos2A-sin2A】的值谢
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2020-04-06 02:03
【已知sin(A+π/4)+sin(A-π/4)=根号2/31.求sinA的值2.求【sin(A-π/4)】/【1-cos2A-sin2A】的值谢】
已知sin(A+π/4)+sin(A-π/4)=根号2/31.求sinA的值2.求【sin(A-π/4)】/【1-cos2A-sin2A】的值谢
(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.