tanα=2,求sin(π-α)cos(2π-α)sin(-α+ 3π/2)/tan(-α-π)sin(-π-α)的值
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tanα=2,求sin(π-α)cos(2π-α)sin(-α+ 3π/2)/tan(-α-π)sin(-π-α)的值
sin(π-α)cos(2π-α)sin(-α+ 3π/2)/tan(-α-π)sin(-π-α)
=sinαcosα(-cosα) / (-tanα)sinα
=(cosα)^2 / tanα
=(cosα)^2 / 2
=[(1/2)(1+cos2α)] / 2
=(1/4)(1+cos2α)
=(1/4) + (1/4)×[1-(tanα)^2 / 1+(tanα)^2]
=(1/4) + (1/4)×(-3/5)
=1/10
=sinαcosα(-cosα) / (-tanα)sinα
=(cosα)^2 / tanα
=(cosα)^2 / 2
=[(1/2)(1+cos2α)] / 2
=(1/4)(1+cos2α)
=(1/4) + (1/4)×[1-(tanα)^2 / 1+(tanα)^2]
=(1/4) + (1/4)×(-3/5)
=1/10
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