Multiple choice

$\sin 81^{\circ} + \tan 81^{\circ}$, when expressed in terms of angles between $0^{\circ}$ and $45^{\circ}$, becomes

  1. $\sin 9^{\circ} + \cos 9^{\circ}$
  2. $\cos 9^{\circ} + \tan 9^{\circ}$
  3. $\sin 9^{\circ} + \tan 9^{\circ}$
  4. $\cos 9^{\circ} + \cot 9^{\circ}$
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D Correct answer
Explanation

sin(81) = cos(9). tan(81) = cot(9). Thus, sin(81) + tan(81) = cos(9) + cot(9).

AI explanation

Using the complementary angle identities, we convert the given functions to fit the specified range. We write sin 81 degrees as cos 9 degrees, and we write tan 81 degrees as cot 9 degrees. Substituting these into the original expression gives cos 9 degrees + cot 9 degrees.

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