*sigh* if you don't get the examples in your text, i doubt seeing a full solution here will help. there are bigger underlying problems that you need to fix, that you won't find unless you try them yourself.
....(half angle formula)
now, the first integral is easy, for the second one, use integration by parts, with and in the formula
combine the fractions to get2. lim (1/sinx - 1/x)
(Applied L'Hopital's rule)
(applied L'Hopital's again)