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      Question

      If tanĪø + secĪø = 5, find the value of sinĪø.

      A 12/13 Correct Answer Incorrect Answer
      B 11/10 Correct Answer Incorrect Answer
      C 4/11 Correct Answer Incorrect Answer
      D 17/23 Correct Answer Incorrect Answer

      Solution

      Let t = tanĪø, s = secĪø. Given: t + s = 5 Use identity: secĀ²Īø āˆ’ tanĀ²Īø = 1 ā‡’ (s āˆ’ t)(s + t) = 1 So: (s āˆ’ t) Ɨ 5 = 1 ā‡’ s āˆ’ t = 1/5 Add the two equations: s + t = 5 s āˆ’ t = 1/5 2s = 5 + 1/5 = 25/5 + 1/5 = 26/5 s = 13/5 ā‡’ secĪø = 13/5 ā‡’ cosĪø = 5/13 Now, tanĪø = t = s + t āˆ’ s = 5 āˆ’ 13/5 = (25 āˆ’ 13)/5 = 12/5 So sinĪø = tanĪø Ɨ cosĪø = (12/5) Ɨ (5/13) = 12/13.

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