sin(α-β)cosα-coa(α-β)sinα=2/3 求cos2β和cos4β

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sin(α-β)cosα-coa(α-β)sinα=2/3 求cos2β和cos4β
tan(2x+y)=3,tanx=-5 求tan(x+y)

sin(α-β)cosα-coa(α-β)sinα=2/3
sin[(α-β)-α]=2/3
sin(α-β-α)=2/3
sin(-β)=2/3
-sinβ=2/3
sinβ=-2/3
cos2β
=1-2(sinβ)^2
=1-2*4/9
=1/9
cos4β
=2(cos2β)^2-1
=2*1/81-1
=-79/81
tan(2x+y)=3,tanx=-5 求tan(x+y)
tan(x+y)
=tan[(2x+y)-x]
=[tan(2x+y)-tanx]/[1+tan(2x+y)tanx]
=(3-5)/(1-3*5)
=-2/(-13)
=2/13

求证2sin(α-2β)sin(α+2β)=cos4β-cos2α 2sinα=sinθ+cosθ,sin²β==sinθcosθ.求证cos2β=2cos2α=2cos 已知sin(α-β)cosα-cos(α-β)sinα=3/5,求cos2β 已知sinθ+cosθ=2sinα,sinθcosθ=(sinβ)^2,求证4(cos2α)^2=(cos2β)^2 已知sinθ+cosθ=2sinα,sinθ·cosθ=sin²β,求证：2cos2α=cos2β. 三角数列题：sinθ sinα cosθ成等差数列,sinθ sinβ cosθ为等比数列,求证2COS2α=cos2β 已知sin(α+β)sin(α-β)=3分之1 求cos2β-cos2α的值,4分之1 sin2α方+sinβ方+cos 化简:sin^2αsin^2β+cos^2αcos^2β-1/2cos2αcos2β 化解sin^2αsin^2β+cos^2αcos^2β-1/2cos2αcos2β 化简(sinα)^2*(sinβ)^2+(cosα)^2(cosβ)^2-1/2cos2αcos2β Sin²αSin²β+Cos²αCos²β-1/2Cos2αCos2β 化简：sin²αsin²β+cos²αcos²β-1/2cos2αcos2β