Help with trig proofs. [edit: one remaining]

I'm stumped on three problems that were assigned on a math project for Algebra II/Trig.

**[SOLVED] **1) Express the following function as a single circular sinusoid.

**f(x)=sqrt(3)*sin(2x)+cos(2x)**

2) Prove that if **y1=a1*sin(bx)** and **y2=a2*cos(bx)**, then **A** is an element of the real number and **B** is an element of the real number such that **a1*sin(bx)+a2*cos(bx)=Asin(k(x+B))**. **A** should be in terms of **a1** and **a2**, and there should be only one expression for **B**. Also, state what the constant **k** is equal to.

**[SOLVED, YAY!] **3) Prove that:

(1/2)+cos(x)+cos(2x)+cos(3x)......+cos(nx)=

sin((n+1/2)x)

---------------

2sin(x/2)

I apologize for the bad formatting (don't know how to get MathType into the forum. )

Any help would be greatly appreciated.