Question

I need help with the following proofs.
a.) cos(nθ)=cos((n-2)θ)-2sinθsin((n-1)θ)
b.) (sin(x/2)+sin(x))/(cos(x/2)-cos(x))=cot(x/4)
c.) (sin∝-cos∝+1)/(sin∝+cos∝-1)=(sin∝+1)/cos∝
d.) tan(x/2)=(1-cos(x)+sin(x))/(1+cos(x)+sin(x))