Consider the space curve given by the equation
(a) Find the unit tangent vector T(t) and the equation of the tangent line at t=Pi.
Everytime I attempt this problem I end up with the most despicable derivatives. I have tried to use trigonometric identities to clean up the problem I'm trying to solve a bit but it still leads to unatural results (a huge repetitive derivative computation). Is there some trigonometric identity that I'm missing out on or a trick that could produce results that make sense?