Question

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Answer 1

11.
(tanx+1)/(1-tanx)=2
tanx=1/3
tan2x=2tanx/(1-tan²x)=3/4
原式=4/9

追答

12.
1/cos2a+tan2a=(sin2a+1)/cos2a=(sina+cosa)²/(cos²a-sin²a)
=(sina+cosa)/(cosa-sina)
=(tana+1)/(1-tana)
=2012

13.
sinθ＞0,cosθ＜0
2θ∈(π,2π)
(sinθ+cosθ)/sinθcosθ=2√2
1+sin2θ=8sin²cos²θ=2sin²2θ
→2sin²2θ-sin2θ-1=0
sin2θ=1(舍去)或sin2θ=-1/2
cos2θ=±√3/2
sin(2θ+π/3)=-1/2×1/2±√3/2×√3/2
=-1或1/2

14.
cosa=-4/5=1-2sin²(a/2)
sin²(a/2)=9/10
sin4a*cos2a/(1+cos4a)=2sin2acos²2a/(2cos²2a)=sin2a=2sinacosa=-24/25
所以结果为
-24/25+9/10=-3/50