若sin2x、sinx分别是sinθ与cosθ的等差中项和等比中项,则cos2x的值为:( ) A.1+338 B.1−338 C.1±338 D.1−24
若sin2x、sinx分别是sinθ与cosθ的等差中项和等比中项,则cos2x的值为:( )
A.
B.
C.
D.
A.
1+
| ||
8 |
B.
1−
| ||
8 |
C.
1±
| ||
8 |
D.
1−
| ||
4 |
数学人气:573 ℃时间:2020-03-26 16:15:42
优质解答
依题意可知2sin2x=sinθ+cosθsin2x=sinθcosθ∵sin2θ+cos2θ=(sinθ+cosθ)2-2sinθcosθ=4sin22x-2sin2x=1∴4(1-cos22x)+cos2x-2=0,即4cos22x-cos2x-2=0,求得cos2x=1±338∵sin2x=sinθcosθ∴cos2x=1-2si...
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