已知cos(a-9π/2)=2cos(5π-a),求sin(a-π)+3sin(2π-a)cos(5π+a)的值

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已知cos(a-9π/2)=2cos(5π-a),求sin(a-π)+3sin(2π-a)cos(5π+a)的值
已知cos(a-9π/2)=2cos(5π-a),求sin(a-π)+3sin(2π-a)cos(5π+a)的值

已知cos(a-9π/2)=2cos(5π-a),求sin(a-π)+3sin(2π-a)cos(5π+a)的值
cos(α-9π/2)=cos(a-π/2)=cos(π/2-a)=sina 2cos(5π-α)=2cos(π-a)=-2cosa sina=-2cosa (sina)^2+(cosa)^2=5(sina)^2/4=1 ,(sina)^2=4/5 ,(cosa)^2=1/5.sin(α-π)^2+3sin(2π-α)cos(5π+α) =(sina)^2+3(-sina)(-cosa) =(sina)^2-6(cosa)^2 =4/5-6/5 =-2/5