Need help simplifying this deriv. of a Trig function: (Sin theta) / (1+ cos theta)

[Strat]

Problem: Differentiate (Sin theta) / (1+ cos theta)

Answer: 1/(1+ cos theta)

Here's what I've got:

I apply the quotient rule such that:
[(1+cos theta)(cos theta) + (sin theta)(-sin theta)]/(1+cos theta)^2

Then I multiply it together:
(Cos theta + cos^2 theta - sin^2 theta) / (1+cos theta)^2

I don't know how to simplify this further. I googled trig identities to refresh my memory but I'm still stuck.

 

[Strat]

Nevermind that one. I see I messed up the quotient rule. I do need help simplifying this one though:

Problem: f(theta) = theta cos theta sin theta

Answer: 1/2sin2theta +theta cos 2theta

Here's what I've got:

(1)(cos theta)(sin theta) + (theta)(-sin theta)(sin theta) + (theta)(cos theta)(cos theta)

(cos theta)(sin theta) + theta(cos^2 theta - sin^2 theta)


Not sure where to go from here.

 

[ksdhart2]

Alright, so you've gotten to this point. I agree with all your work thus far.

\(\displaystyle f'(x)=cos(\theta) \cdot sin(\theta) + \theta \left( cos^2(\theta)-sin^2(\theta) \right)\)

But past this, there's not much left to be done, you've done the hard part already. I'm not sure what form your book shows, but my guess is they just cleaned up the result a bit. There's a few identities you seem to have forgotten that will help you out. Try this page from SOSMath for a refresher, particularly the double angle identities.