In Exercises 33–42, let sin t = a, cos t = b, and tan t = c. Write each expression in terms of a, b, and c. tan(-t) - tan t

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Recall the identity for the tangent of a negative angle: \(\tan(-t) = -\tan t\).

Substitute the given value \(\tan t = c\) into the expression: \(\tan(-t) - \tan t = -c - c\).

Combine like terms: \(-c - c = -2c\).

Express the final result in terms of \(a\), \(b\), and \(c\). Since the expression only involves \(c\), the answer is \(-2c\).

Thus, the expression \(\tan(-t) - \tan t\) simplifies to \(-2c\) using the given definitions.

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