Starting with the Identity $\sin ^ { 2 } x + \cos ^ { 2 } x = 1$

Essay

Starting with the identity $\sin ^ { 2 } x + \cos ^ { 2 } x = 1$ and then dividing both sides of the equation by a suitable trigonometric function, derive the trigonometric identity.
​ $\sec ^ { 2 } x = 1 + \tan ^ { 2 } x$