已知sin(π/4+α)*sin(π/4-α)=1/4,α∈(π/4,π/2),求2sin^α+tanα-cotα-1的值

来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/28 19:54:42
已知sin(π/4+α)*sin(π/4-α)=1/4,α∈(π/4,π/2),求2sin^α+tanα-cotα-1的值已知sin(π/4+α)*sin(π/4-α)=1/4,α∈(π/4,π/2)

已知sin(π/4+α)*sin(π/4-α)=1/4,α∈(π/4,π/2),求2sin^α+tanα-cotα-1的值
已知sin(π/4+α)*sin(π/4-α)=1/4,α∈(π/4,π/2),求2sin^α+tanα-cotα-1的值

已知sin(π/4+α)*sin(π/4-α)=1/4,α∈(π/4,π/2),求2sin^α+tanα-cotα-1的值
sin(π/4+α)*sin(π/4-α)
=sin(π/4+α)*cos(π/4-α)
=1/2sin(π/2+2α)
=1/2cos2α
1/2cos2α=1/4
cos2α=1/2 α∈(π/4,π/2),
所以2α=π/3
2sin^α+tanα-cotα-1
=2sin^α-1+sinα/cosα-cosα/sinα
=-cos2α+(sin^α-cos^α)/sinαcosα
=-cos2α-cos2α/(sin2α/2)
=-(cos2α+2cot2α)
=-(cosπ/3+2cotπ/3)
=-(1/2+2√3/3)
=-2√3/3-1/2

（根号2/2）^2*(cosa-sina)(cosa+sina)=1/2
所以C^2-S^2=1/2,又C^2+S^2=1 α∈(π/4,π/2)
所以C=根号3/2，S=1/2，即α=π/6
2sin^α+tanα-cotα-1
=1/2+根号3/3-根号3-1
=……

已知sin(α+π/3)+sinα=-4√3/5(-π/2 已知sinα=﹣4/5,求√2 sin(α+π/4)的值 已知sin=1/4,π/2 sin(α-π/4)=12/13,sinα= 已知sinα=4/5,求下列三角函数值1）sin（-α）2）sin（π-α）3）sin（π+α）4）sin（2π-α） 已知sin(α+π/4)=3/5,π/2 已知-π/6≤β≤＜π/4,3sin²α-2sin²β=2sinα,求sin²β-½sinα的最小值 已知-π/6＜=β＜π/4,3sin^2α-2sin^2β=2sinα,求sin^2β-1/2sin^2α的最值. 已知β∈[-π/6,π/4）,且3（sinα）^2-2（sinβ）^2=2sinα,求（sinβ）^2-1/2sinα的最小值 已知sin(π/4-α)=5/13,0 已知sin(π/4-α)=5/13,0 已知sinα =4/5,π/2 已知sin(（π/4）-α)=5/13,(0 已知sin(45度-α)=-2/3,π/4 已知sin=-4/5,π＜α 化简sin(π/4+α)cosα-sin(π/4-α)sinα 已知sin(π+θ) sin(x+π/4)