Question

complete the sentence so the result is an identity. let x be any real number.
___ + \\( \tan ^ { 2 } x = \sec ^ { 2 } x \\)

a. \\( \sin ^ { 2 } x \\)
b. \\( \cos ^ { 2 } x \\)
c. 1
d. -1

Explanation:

Step1: Recall the Pythagorean identity

We know the fundamental Pythagorean identity in trigonometry: \(1+\tan^{2}x=\sec^{2}x\). This identity is derived from the basic definitions of \(\tan x=\frac{\sin x}{\cos x}\) and \(\sec x = \frac{1}{\cos x}\).

Starting with \(\sin^{2}x+\cos^{2}x = 1\). Divide each term by \(\cos^{2}x\):

$$
LATEXBLOCK0
$$

Answer:

C. 1