"The expression given matches the pattern of the formula for"
sin( x + y ). \ \ "Recall that formula:"
\qquad \qquad \qquad \qquad \quad \quad sin( x + y ) \ = \ sinx cosy + cos x siny.
"Now write it in the reverse direction:"
\qquad \qquad \qquad \qquad \quad \quad sinx cosy + cos x siny \ = \ sin( x + y ).
"Now, if in the reverse direction of that formula, we let:"
\qquad \qquad \qquad \qquad \qquad \qquad \qquad x = 15^@ \qquad "and" \qquad y = 75^@;
"we get:"
\qquad \qquad \quad sin15^@ cos75^@ + cos 15^@ sin75^@ \ = \ sin( 15^@ + 75^@ ).
"Thus:"
\qquad \qquad \quad sin15^@ cos75^@ + cos 15^@ sin75^@ \ = \ sin( 90^@ ) \ = \ 1.
"So we have the following simplification result:"
\qquad \qquad \qquad \qquad \quad sin15^@ cos75^@ + cos 15^@ sin75^@ \ = \ 1.