三个三角题~~~~~~~~~~

1 证明 tan(1.5x)-tan(0.5x)=(2sinx)/(cosx+cos2x)

2 已知 sin(x-3π/4)cos(x-π/4)=-1/4 求cos4x的值

3 已知 sin(π/4+α)sin(π/4-α)=1/6  α∈(π/2,π) 求sin4α

详细 蟹蟹^.^

1，用Tanx/2=sinx/(1+cosx)把tanx写成sinx/cosx 就可以证出。

2，sin(x-3π/4)=-sin(x-π/4)所以-2sin(x-π/4)cos(x-π/4)=-1/2所以sin（2x-π/2）=1/2 cos2x=-1/2

3,把 sin(π/4+α)sin(π/4-α)=1/6 拆开，得到cos2x=1/3.因为α∈(π/2,π) ，所以sin2x＜0所以sin4x就可求出

(1)sin1.5x/cos1.5x--sin0.5x/cos0.5x=(sin1.5x*cos0.5x-sin0.5x*cos1.5x)/cos1.5x*sin0.5x

=sinx/cos(x+0.5x)*cos0.5x=sinx/(1/2)*(cosx+cos^2x-sin^2x)=2sinx/(cosx+cos2x)

2.sin(x-3π/4)cos(x-π/4)=sin(x-π/4-π/2)cos(x-π/4)=-cos^2(x-π/4)=-1/4

==>cos(2x-π/2)=-1/2==>sin2x=-1/2==>cos^22x=3/4==>cos4x=1   注 (cos^2x=(1+cos2x)/2)

3.和2同理