For integer n, an is difined by a_n\equal{}\int_0^{\frac{\pi}{4}} (\cos x)^ndx.
(1) Find a_{\minus{}2},\ a_{\minus{}1}.
(2) Find the relation of an and a_{n\minus{}2}.
(3) Prove that a_{2n}\equal{}b_n\plus{}\pi c_n for some rational number bn, cn, then find cn for n<0. calculusintegrationtrigonometrylogarithmscalculus computations