Question

prove the identity.

\\((\csc^2 x - 1)\sec x = \cot x \csc x\\)

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statement
\\((\csc^2 x - 1)\sec x\\)

reason
select
algebraic transformation
reciprocal identities
quotient identities
pythagorean identities
odd and even identities

Explanation:

Apply Pythagorean identity to the expression

$$ \csc^2 x - 1 = \cot^2 x $$

Substitute and simplify the product

$$ (\csc^2 x - 1)\sec x = \cot^2 x \sec x $$

Identify the matching reason

The transformation uses the Pythagorean identity \(\cot^2 x + 1 = \csc^2 x\).

Answer:

• Statement: \(\cot^2 x \sec x\)
• Reason: Pythagorean identities