posted in the wrong section.
for the first question, this is integration - you can use "cos(2x)=2(cosx)^2 - 1" etc. identities help with the integration.
for the second question, you wish to rearrange to find (T_2/T_1), you should take exponentials and then 'collect terms'.
for the third question, on first glance this cannot be solved without further assumptions.