Question

已知cos阿尔法=－五分之四,且阿尔法为第三象限角.1,求sin（阿尔法＋三分之派）的值.

Answer 1

1) cosα =-4/5,且α为第三象限角

==>sinα=-3/5

sin(α+π/3)=sinα*(1/2)+cosα *(√3/2)

=-3/5*(1/2)+(-4/5)*(√3/2)=(3-4√3)/10

2) [2sin(π/4+α)sin(π/4-α)]/sin(π-2α)

=2sin(π/4+α)cos(π/4+α)/sin(2α)

=sin2(π/4+α)/sin(2α)=sin(π/2+2α)/(sin2α)

=cos2α/sin2α

cosα =-4/5,sinα=-3/5==>sin2α=2*(-3/5)*(-4/5)=24/25

cos2α=2cos²α-1=2*(16/25)-1=7/25

[2sin(π/4+α)sin(π/4-α)]/sin(π-2α)=cos2α/sin2α=7/24