1 已知sin(90°+α)sin(90°-α)=1/6,且α∈(90°,180°),求sin4α的值
问题描述:
1 已知sin(90°+α)sin(90°-α)=1/6,且α∈(90°,180°),求sin4α的值
2 已知sin(90°-α)=(7√2)/10,cos2α=7/25,求sinα及tan(α+60°)的值>
答
1.sin(90°+α)sin(90°-α)=cosαcosα=cosα^2=1/6所以sinα^2=1-cosα^2=5/6sin4α=2sin2αcos2α=4sinαcosα(cosα^2-sinα^2)=4sinαcosα(1/6-5/6)=-4sinαcosα×4/6=-8/3sinαcosα因为α∈(90°,180°)所...