Determining the trigonometrical problem using Sin (A + B) formula

\[\color {purple} {Example\ 1:}\ \color {red} {Find\ the\ value\ of}\ sin\ {50}^0\ cos\ {40}^0\ +\ cos\ {50}^0\ sin\ {40}^0\ \hspace{15cm}\]

\[\color {blue}{Solution:}\ W.\ K.\ T\ Sin ( A + B )\ =\ Sin A\ Cos B\ +\ Cos A\ Sin B\ \hspace{18cm}\]

\[sin\ {50}^0\ cos\ {40}^0\ +\ cos\ {50}^0\ sin\ {40}^0\ =\ Sin\ ({50}^0\ + {40}^0)\ \hspace{10cm}\]

\[=\ Sin \ {90}^0\ \hspace{10cm}\]

\[=\ 1\ \hspace{10cm}\]

\[\boxed{\therefore\ sin\ {50}^0\ cos\ {40}^0\ +\ cos\ {50}^0\ sin\ {40}^0\ =\ 1}\]