已知sin(π+α)=1/4,求sin(2π-α)-cot(α-π)cosα的值
问题描述:
已知sin(π+α)=1/4,求sin(2π-α)-cot(α-π)cosα的值
答
sin(π+α)=1/4,sina=-1/4sin(2π-α)-cot(α-π)cosα=-sina+cot(∏-a)cosa=-sina-cotacosa=-sina-cosa/sina*cosa=1/4-(cosa)^2/(-1/4)=1/4+4[1-(sina)^2]=1/4+4(1-1/16)=4