Question

prove the identity.

\\(\sec^2 x - 1) \cos x = \sin^2 x \sec x\\

statement:
\\(\sec^2 x - 1) \cos x\\

reason: pythagorean identities

Explanation:

Apply the Pythagorean identity

Using the Pythagorean Identities knowledge point

$$ \sec^2 x - 1 = \tan^2 x $$

Substitute and simplify the expression

Using the Trigonometric Identities knowledge point

$$
LATEXBLOCK0
$$

Identify the correct step for the proof

Using the Pythagorean Identities knowledge point

$$ (\sec^2 x - 1)\cos x = \tan^2 x \cos x $$

Answer:

Prove the identity:

$$ (\sec^2 x - 1)\cos x = \sin^2 x \sec x $$

Statement	Reason
\( = \) <blank>\(\tan^2 x \cos x\)</blank>	Pythagorean identities