Code: Select all
\begin{equation*}
\begin{split}
T(f+g)=(f+g)(tg(\pi x-\frac{\pi}{2}))\cdot\Bigl( (\frac{\pi}{cos^{2}(\pi x-\frac{\pi}{2})}\Bigr)^{\frac{1}{p}}=
& f(tg(\pi x-\frac{\pi}{2}))\cdot\Bigl( (\frac{\pi}{cos^{2}(\pi x-\frac{\pi}{2})}\Bigr)^{\frac{1}{p}}+
& g(tg(\pi x-\frac{\pi}{2}))\cdot\Bigl( (\frac{\pi}{cos^{2}(\pi x-\frac{\pi}{2})}\Bigr)^{\frac{1}{p}}=
& Tf+Tg
\end{split}
\end{equation*}