Triple angle formula?

Question

g-day i am trying to derive the triple angle formula (cos3t) but have run into some trouble pretty early on. Could someone please help me. This is what i have done so far. Thanks heaps

cos(3t) = cos(2t+2)

= cos(2t)*cos(t) - sin(2t)*sin(t)

= -2sin(t)^2cos(t)+2*cos^3(t)-cos(t)

= -2(1-cos(2t)/2)*cos*t) + 2cos^3(t)-cos(t)

Answer 1

Though you can proceed with cos 3t = cos (2t + t), the best method is as under.

cos 3t

= cos3t + cos t - cost

= 2cos(3t + t)/2 cos(3t - t)/2 - cost

= 2cos 2t cost - cost

= 2(2cos² t - 1)cost - cost

= 4cos³ t - 3cost

Answer 2

Your first step is correct. second should be

[2cos^2t -1]cost - 2sintcost(sint)

= 2cos^3t - cost - 2(1- cos^2t)cost.

= 4cos^3t - 3cost, which is the formula.