Answer
The correct use of the Pythagorean Identity:
$1+tan^2\theta=sec^2~\theta$
If $\theta=60°$:
$1+tan~60°=1+\sqrt 3\ne sec~60°=2$
Work Step by Step
$1+tan~\theta=1+\frac{sin~\theta}{cos~\theta}=\frac{cos~\theta+sin~\theta}{cos~\theta}\ne sec~\theta=\frac{1}{cos~\theta}$
