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>

Question

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>

Answer 1

1.sin(90°+α)sin(90°-α)=cosαcosα=cosα^2=1/6所以sinα^2=1-cosα^2=5/6
sin4α=2sin2αcos2α=4sinαcosα(cosα^2-sinα^2)=4sinαcosα(1/6-5/6)
=-4sinαcosα×4/6=-8/3sinαcosα
因为α∈(90°,180°)所以sinα>0,cosα