"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).
