已知sin(a-π/4)=(7√2)/10,cos2a=7/25(1)求sina+cosa(2)求tan(a+π/3)

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已知sin(a-π/4)=(7√2)/10,cos2a=7/25(1)求sina+cosa(2)求tan(a+π/3)

已知sin(a-π/4)=(7√2)/10,cos2a=7/25(1)求sina+cosa(2)求tan(a+π/3)
已知sin(a-π/4)=(7√2)/10,cos2a=7/25
(1)求sina+cosa
(2)求tan(a+π/3)

已知sin(a-π/4)=(7√2)/10,cos2a=7/25(1)求sina+cosa(2)求tan(a+π/3)
∵sin(a-π/4)=(7√2)/10
∴sinacosπ/4-cosasinπ/4 =(7√2)/10
∴√2/2(sina-cosa)=(7√2)/10
∴sina-cosa=7/5 .(1)
∵cos2a=7/25
∴cos^2a-sin^2a=7/25
∴sin^2a-cos^2a=-7/25
∴(sina+cosa)(sina-cosa)=-7/25 .(2)
(2)÷(1)得:
sina+cosa=-7/25÷7/5=-1/5 .(3)
(3)+(1):2sina=6/5,sina=3/5
(3)-(1):2cosa=-8/5,cosa=-4/5
tana=sina/cosa=-3/4
tan(a+π/3)=(tana+tanπ/3)/(1-tanatanπ/3)
= (-3/4+√3)/(1-(-3/4)√3)
=(4√3-3)/(4+3√3)
=(4√3-3)(3√3-4)/{(3√3)^2-4^2}
=(48-25√3)/11