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sin2a=3√7/8,
a∈[兀/4,兀/2],
2a∈[兀/2,兀],cos2a<0,cos2a=-√[1-(sin2a)^2]=-1/8
cos2a=1-2(sina)^2,2(sina)^2=1+1/8=9/8
(sina)^2=9/16
sina =3/4
--------------
(sina)^2+(cosa)^2 = 1
sin2a= 2sina * cosa
(sin2a)^2=(3/8)^2 * 7=63/64 = 4sina * sina * cosa *cosa
(sina)^2 * (cosa)^2 =63/256
(sina)^2 * [1-(sina)^2 ]=63/256
设(sina)^2=t
t-t^2=63/256,
(t-9/16)(t-7/16)=0
(sina)^2 = 9/16 或7/16,
a∈[四分之兀,二分之兀],sina ≥√2/2=√8/4,(sina)^2 ≥1/2=8/16.
(sina)^2 = 9/16
sina =3/4
不懂追问
a∈[兀/4,兀/2],
2a∈[兀/2,兀],cos2a<0,cos2a=-√[1-(sin2a)^2]=-1/8
cos2a=1-2(sina)^2,2(sina)^2=1+1/8=9/8
(sina)^2=9/16
sina =3/4
--------------
(sina)^2+(cosa)^2 = 1
sin2a= 2sina * cosa
(sin2a)^2=(3/8)^2 * 7=63/64 = 4sina * sina * cosa *cosa
(sina)^2 * (cosa)^2 =63/256
(sina)^2 * [1-(sina)^2 ]=63/256
设(sina)^2=t
t-t^2=63/256,
(t-9/16)(t-7/16)=0
(sina)^2 = 9/16 或7/16,
a∈[四分之兀,二分之兀],sina ≥√2/2=√8/4,(sina)^2 ≥1/2=8/16.
(sina)^2 = 9/16
sina =3/4
不懂追问
展开全部
cos2a=-(1/8) (cosa)²-(sina)²=-(1/8) (cosa)²+(sina)²=1 (sina)²=(9/16) sina= 3/4
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