求证cos(3π/2+α)=sinα

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求证cos(3π/2+α)=sinα
求证cos(3π/2+α)=sinα

求证cos(3π/2+α)=sinα
cos(3π/2+α)=cos[π+(a+π/2)]=-cos(a+π/2)=sina
所以得证
根据诱导公式

cos(3π/2+α)
=sin[π/2-(3π/2+α)]
=sin(-π-a)
=-sin(-α)
=sinα

cos(3π/2+α)
=cos(3π/2+a-2π)
=cos(a-π/2)
=cos(π/2-a)
=sinα

cos(3π/2+α)=cos[π+(a+π/2)]=-cos(a+π/2)=sina

这也要证明。

cos(3π/2+α)=cos3π/2cosα-sin3π/2sinα=0-(-1sinα)=sinα

cos(3π/2+α)=sin[π/2-(3π/2+α)]=sin(π/2-3π/2-α)=sin(-π-α)=-sin(π+α)=sinα