Final answer:
To solve the provided trigonometric identity, the definitions of tan(x), sec(x), and csc(x) in terms of sides of a right triangle must be used, as well as trigonometric identities like the Pythagorean identity. None of the options provided can be validated without proper mathematical formatting or symbols.
Step-by-step explanation:
A student has asked about a trigonometric identity involving tan(x), sec(x), and csc(x) for an acute angle x. The question seems to be malformed, but we can offer some clarity on what constitutes valid trigonometric identities. For the given trigonometric functions, recall that tan(x) = sin(x)/cos(x), sec(x) = 1/cos(x), and csc(x) = 1/sin(x). In the context of a right triangle, defined in terms of its sides: if x is the adjacent side, y is the opposite side, and h is the hypotenuse, then we have tan(x) = y/x, sec(x) = h/x, and csc(x) = h/y, following the definitions provided in Figure 5.17. To verify any of the trigonometric identity options presented, you would need to manipulate these definitions and make use of trigonometric identities such as the Pythagorean identity, sin2(x) + cos2(x) = 1, which can be transformed to derive sec2(x) = 1 + tan2(x) or csc2(x) = 1 + cot2(x). The right answer will be one where both sides of the equation are simplified or transformed to be the same. However, without the proper formatting or correct mathematical symbols, it is not possible to definitively determine which, if any, of the given options is correct.