化简sin(α-5π)/cos(3π-α)×cos(π/2-α)/sin(α-3π)×cos(8π-α)/sin(-α-4π)

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化简sin(α-5π)/cos(3π-α)×cos(π/2-α)/sin(α-3π)×cos(8π-α)/sin(-α-4π)

化简sin(α-5π)/cos(3π-α)×cos(π/2-α)/sin(α-3π)×cos(8π-α)/sin(-α-4π)
化简sin(α-5π)/cos(3π-α)×cos(π/2-α)/sin(α-3π)×cos(8π-α)/sin(-α-4π)

化简sin(α-5π)/cos(3π-α)×cos(π/2-α)/sin(α-3π)×cos(8π-α)/sin(-α-4π)
原式=sin(α-π)/cos(π-α)× sinα/sin(α-π)× cos(-α)/sin(-α)
=sin[-(π-α)]/(-cosα)× sinα/(-sinα)× cosα/sinα
=(-sinα)/(-cosα)× (-1)× cosα/sinα
=1
【本题考查的是诱导公式】
【基本的原理过程已经详细写出,如有不懂请追问.】

等于1,记住奇“变偶不变,符号看象限”再化简就行了

原式=sin(α-π)/cos(π-α)× sinα/sin(α-π)× cos(-α)/sin(-α)
=sin[-(π-α)]/(-cosα)× sinα/(-sinα)× cosα/sinα
=(-sinα)/(-cosα)× (-1)× cosα/sinα
=1

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