Tg²a +1 = sec²a

The equation you provided is a well-known trigonometric identity. It can be derived from the Pythagorean identities in trigonometry.

The identity states:

\[ \tan^2(a) + 1 = \sec^2(a) \]

Here's a brief derivation:

1. We start with the basic Pythagorean identity: \[ \sin^2(a) + \cos^2(a) = 1 \]

2. By dividing each term by \(\cos^2(a)\), we get: \[ \frac{\sin^2(a)}{\cos^2(a)} + \frac{\cos^2(a)}{\cos^2(a)} = \frac{1}{\cos^2(a)} \]

3. This simplifies to: \[ \tan^2(a) + 1 = \sec^2(a) \]

Thus, your equation \( \tan^2(a) + 1 = \sec^2(a) \) is indeed correct! This identity is commonly used in various trigonometric problems and calculus, particularly when dealing with integrals and derivatives involving tangent and secant functions.