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      Question

      If sec a + tan a = 3/2, find the value of sin a. 

      A 5/13 Correct Answer Incorrect Answer
      B 12/13 Correct Answer Incorrect Answer
      C 13/12 Correct Answer Incorrect Answer
      D 5/12 Correct Answer Incorrect Answer

      Solution

      Given, sec a + tan a = (3/2) ..............(I)   We know that, sec² a - tan² a = 1   Or, (sec a + tan a) (sec a - tan a) = 1   So, sec a - tan a = (2/3) ...........(II)   On adding equations (I) and (II), we get;   2 sec a = (3/2) + (2/3) = (9 + 4)/6 = (13/6)  Or, sec a = (13/12)   So, cos a = [1/(sec a)] = (12/13)   So, sin a = √[1 - (12/13)²] = √(25/169) = (5/13)   Hence, sin a = (5/13)

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