问题标题:
【已知A(-2,α)是角α终边上的一点,且sinα=-√5/5,求[cos(π/2+α)sin(-π-α)]/[cos(11π/2-α)sin(9π/2+α]】
问题描述:
已知A(-2,α)是角α终边上的一点,且sinα=-√5/5,求[cos(π/2+α)sin(-π-α)]/[cos(11π/2-α)sin(9π/2+α]
毛大恒回答:
[cos(π/2+α)sin(-π-α)]/[cos(11π/2-α)sin(9π/2+α]=
[sinαsinα]/[cos(5π+π/2-α)sin[4π+π/2+α]=
sinα^2/[cos(π/2-α)sin(π/2+α)]=sinα^2/[sinα(-α)cosα)]=
sinα^2/[-sinαcosα]=-sinα/cosα=-tanα=-1/2
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