Question

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Explanation:

Identify the trigonometric ratio for \(\tan(\angle R)\)

Using the Trigonometric Ratios knowledge point

$$ \tan(\angle R) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{PQ}{PR} $$

Relate \(\angle R\) and \(\angle Q\) using complementary angles

Using the Trigonometric Ratios knowledge point

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Express \(\tan(\angle R)\) in terms of sine and cosine

Using the Trigonometric Ratios knowledge point

$$ \tan(\angle R) = \frac{\sin(\angle R)}{\cos(\angle R)} $$

Identify equivalent expressions from standard options

Using the Trigonometric Ratios knowledge point

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Answer:

Based on the right triangle \(\triangle PQR\) with the right angle at vertex \(P\), the expressions equivalent to \(\tan(\angle R)\) are:

1. \(\frac{PQ}{PR}\) (the ratio of the opposite side to the adjacent side)
2. \(\frac{\sin(\angle R)}{\cos(\angle R)}\) (the quotient identity for tangent)