The trigonometric expression tan² x + 1 = sec² x is proved by using the fundamental trigonometric formula and the definition of tangent and secant.
<h3>How to prove a derivate trigonometric formula</h3>
In this problem we must prove the existence of a trigonometric formula by means of definitions of trigonometric functions and the fundamental trigonometric formula.
Step 1 - Introduce the fundamental trigonometric formula and the definitions of tangent and secant:
sin² x + cos² x = 1, tan x = sin x / cos x, sec x = 1 / cos x
Step 2 - Divide each side of the formula by cos² x:
sin² x / cos² x + cos² x / cos² x = 1 / cos² x
(sin x / cos x)² + 1 = (1 / cos x)²
Step 3 - Use the definition of the two trigonometric functions:
tan² x + 1 = sec² x
To learn more on trigonometric functions: brainly.com/question/14746686
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