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 ify1=a1*sin(bx)andy2=a2*cos(bx), thenAis an element of the real number andBis an element of the real number such thata1*sin(bx)+a2*cos(bx)=Asin(k(x+B)).Ashould be in terms ofa1anda2, and there should be only one expression forB. Also, state what the constantkis equal to.

[SOLVED, YAY!]3) Prove that:I apologize for the bad formatting (don't know how to get MathType into the forum. )

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

sin((n+1/2)x)

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

2sin(x/2)

Any help would be greatly appreciated.