# "We are asked to prove:" #
# \qquad \qquad \qquad \qquad \qquad { 1+ 2 sinx cosx } / { sinx + cosx } \ = \ sinx + cosx. #
# "Looking at the LHS, we have the following:" #
# \qquad { 1+ 2 sinx cosx } / { sinx + cosx } \ = \ { ( sin^2x + cos^2x )+ 2 sinx cosx } / { sinx + cosx } #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ = \ { sin^2x + 2 sinx cosx + cos^2x } / { sinx + cosx } #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ = \ ( sinx + cosx )^2 / { sinx + cosx } #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ = \ sinx + cosx. #
# \qquad :. \qquad \qquad \qquad \qquad { 1+ 2 sinx cosx } / { sinx + cosx } \ = \ sinx + cosx. \qquad \qquad \qquad \qquad \ \ (!) #