Supposed that f(x) has f′(x) and for any real numbers x, y, \int_y^{x \plus{} y} f(t)\ dt \equal{} \int_0^x \{f(y)\cos t \plus{} f(t)\cos y\}\ dt holds.
(1) Express f(x \plus{} y) in terms of f(x), f(y).
(2) Find f'\left(x \plus{} \frac {\pi}{2}\right). Note that f\left(\frac {\pi}{2}\right) \equal{} 2.
(3) Find f(x). calculusintegrationtrigonometrycalculus computations