已知cos(π/2+α )=2sin(α -π/2) 求sin^3(π-α )+cos(α -π)/5cos(5π/2-α )+3sin(7π/2-α )

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已知cos(π/2+α )=2sin(α -π/2) 求sin^3(π-α )+cos(α -π)/5cos(5π/2-α )+3sin(7π/2-α )
已知cos(π/2+α )=2sin(α -π/2) 求sin^3(π-α )+cos(α -π)/5cos(5π/2-α )+3sin(7π/2-α )

已知cos(π/2+α )=2sin(α -π/2) 求sin^3(π-α )+cos(α -π)/5cos(5π/2-α )+3sin(7π/2-α )
cos(π/2+α )=2sin(α -π/2)

-sina=-2cosa
tana=2
sin^3(π-α )+cos(α -π)/5cos(5π/2-α )+3sin(7π/2-α )
=(sin^3a-cosa)/(5sina-3cosa) (上下同除cosa)
=(sin^2a*tana-1)/(5tana-3)
=(2sin^2a-1)/7
=1/7*(sin^2a-cos^2a)/(sin^2a+cos^2a) (上下同除cos^2a)
=1/7*(tan^2a-1)/(tan^2a+1)
=3/35