已知tan(90°-α)=-1/4.若α是第二象限角,先化简sin(180°-α)sin(270...
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发布时间：2024-10-23 22:45
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时间：2024-11-07 00:24
解：∵α是第二象限角
∴cosα<0
∵tan(90°-α)=-1/4
==>cotα=-1/4
==>cosα/sinα=-1/4
==>sinα=-4cosα
==>(-4cosα)^2+(cosα)^2=1
==>(cosα)^2=1/17
∴cosα=-1/√17
故[sin(180°-α)sin(270°-α)tan(90°-α)]/[sin(90°+α)tan(270°+α)tan(360°-α)]
=[sinα(-cosα)cotα]/[cosα(-cotα)(-tanα)] (应用诱导公式)
=-(cosα)^2/cosα
=-cosα
=-(-1/√17)
=1/√17。
