VERY URGENT! PLEASE HELP SOLVE!

Question

tan(x)+1=sqrt(3)+sqrt(3)cot(x)as well as

sin(2x)= 2 cos^(x)

4cos2(x) = 8sin(x)cos(X)

Answer 1

1)sin(x)/cos(x)+1=sqrt(3)(1+cos(x)/sin(x))
(sin(x)+cos(x))/cos(x)=
=sqrt(3)(sin(x)+cos(x))/sin(x)
1/cos(x)=sqrt(3)/sin(x)
tan(x)=sqrt(3)
x=Pi/3+Pi*n

2)cos^(x)---???

3)cos2(x)=cos(2x) or cos^2(x)?