for the function $f \in L^2 ([-\pi,\pi])$ define the map $ T: L^2([-\pi, \pi]) \to R $ as $T(f)=a_1+b_1 $ if the Fourier series of $f$ is of the form
$f $ ~ $a_0 +\sum_{n=1}^{\infty} (a_ncos(nx)+b_nsin(nx)) $ by finding function $h \in L^2 ([-\pi,\pi])$ so that $T(f)=\int_{-\pi}^\pi f(x)h(x)dx $
$ a_0:=\frac1{2\pi}\int_{-\pi}^\pi f(x)\,\mathrm d x\\ a_n:=\frac1{\pi }\int_{-\pi }^\pi f(x)\cos(nx)\,\mathrm d x\\ b_n:=\frac1{\pi }\int_{-\pi }^\pi f(x)\sin(nx)\,\mathrm d x$
and eventually found $h(x)=\frac1{\pi }(\cos (x)+\sin(x)) $
how can i compute $ ||T||$ ? I tried to calculate, however got big integral and got confused, is there anyway to nicely compute it?