已知tanθ=2求2cosθ-4sinθ/5cosθ+3sinθ和 3sin-2θ-4cos2θ
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已知tanθ=2求2cosθ-4sinθ/5cosθ+3sinθ和 3sin-2θ-4cos2θ
已知tanθ=2求2cosθ-4sinθ/5cosθ+3sinθ和 3sin-2θ-4cos2θ
已知tanθ=2求2cosθ-4sinθ/5cosθ+3sinθ和 3sin-2θ-4cos2θ
(2cosθ-4sinθ)/(5cosθ+3sinθ)
=(2cosθ-4cosθ·tanθ)/(5cosθ+3cosθ·tanθ)
=(2-4tanθ)/(5+3tanθ)
=(2-4×2)/(5+3×2)
=-6/11,
3sin(-2θ)-4cos2θ
=-6sinθ·cosθ-4(cos²θ-sin²θ)
=(-6sinθ·cosθ-4cos²θ+4sin²θ)/(sin²θ+cos²θ)
=(-6tanθ·cos²θ-4cos²θ+4tan²θ·cos²θ)/(tan²θ·cos²θ+cos²θ)
=(-6tanθ-4+4tan²θ)/(tan²θ+1)
=(-6×2-4+4×2²)/(2²+1)
=0.
若3sin²θ-4cos²θ
=(3sin²θ-4cos²θ)/(sin²θ+cos²θ)
=(3tan²θ-4)/(tan²θ+1)
=(3×2²-4)/(2²+1)
=8/5
22
（2cosθ-4sinθ）/（5cosθ+3sinθ）
=[(2cosθ-4sinθ)÷cosθ]/[(5cosθ+3sinθ)÷cosθ]
=[2-4tanθ]/[5+3tanθ]
=[2-4×2]/[5+3×2]
=-6/11
3sin2θ-4cos2θ
=6sinθcosθ-4(2cos²θ-1)
=6sinθcosθ-8co...
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（2cosθ-4sinθ）/（5cosθ+3sinθ）
=[(2cosθ-4sinθ)÷cosθ]/[(5cosθ+3sinθ)÷cosθ]
=[2-4tanθ]/[5+3tanθ]
=[2-4×2]/[5+3×2]
=-6/11
3sin2θ-4cos2θ
=6sinθcosθ-4(2cos²θ-1)
=6sinθcosθ-8cos²θ+4
=(6sinθcosθ-8cos²θ)/(sin²θ+cos²θ)+4
=[(6sinθcosθ-8cos²θ)÷cos²θ]/[(sin²θ+cos²θ)÷cos²θ]+4
=[6tanθ-8]/[tan²θ+1]+4
=[6×2-8]/[2²+2]+4
=4/6+4
=2/3+4
=4又2/3
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