已知tanα=2,求sin(π/4+α)/cos(π/4+α)·tan2α的值

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已知tanα=2,求sin(π/4+α)/cos(π/4+α)·tan2α的值
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已知tanα=2,求sin(π/4+α)/cos(π/4+α)·tan2α的值
已知tanα=2,求sin(π/4+α)/cos(π/4+α)·tan2α的值

已知tanα=2,求sin(π/4+α)/cos(π/4+α)·tan2α的值
tan2a=[2tana]/[1-tan²a]=-4/3
sin(π/4+a)/cos(π/4+a)
=[sin(π/4)cosa+cos(π/4)sina]/[cos(π/4)cosa-sin(π/4)sina]
=[cosa+sina]/[cosa-sina]
=[1+tana]/[1-tana]
=-3
则:原式=[-3]/[-4/3]=9/4

sin(π/4+α)/cos(π/4+α)·tan2α=(tana+1)/(tan-1) *[2tana/(1-tana的平方)]