# "We are asked to see if the following is true:" #
# \qquad \qquad \qquad \qquad cos^2(\theta) \ + \ sin^2(\theta) \ = \ sec(\theta) cos(\theta). \qquad \qquad \qquad \qquad \qquad \qquad \ \ (1) #
# "We can look at each side of this statement separately." #
# "LHS of (1):" \qquad \qquad \qquad cos^2(\theta) \ + \ sin^2(\theta) \ = \ 1; #
# \qquad \qquad \qquad \qquad \qquad "by Fundamental Pythagorean Identity." #
# "RHS of (1):" \qquad \quad sec(\theta) cos(\theta) \ = \ 1/cos(\theta) cos(\theta) \ = \ 1; #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad "by Reciprocal Identities." #
# "So we conclude:" #
# \qquad \qquad \qquad \qquad \qquad \qquad \qquad "LHS of (1)" \ = \ "RHS of (1)." #
# "Thus our statement in (1) is true, it is a trig identity:" #
# \qquad \quad "True:" \qquad \quad \quad cos^2(\theta) \ + \ sin^2(\theta) \ = \ sec(\theta) cos(\theta). #
