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      Question

      If sec a + tan a = 5/2, find the value of sin a. 

      A 20/29 Correct Answer Incorrect Answer
      B 21/29 Correct Answer Incorrect Answer
      C 29/20 Correct Answer Incorrect Answer
      D 29/10 Correct Answer Incorrect Answer

      Solution

      Given, sec a + tan a = (5/2) ..............(I)   We know that, sec² a - tan² a = 1  Or, (sec a + tan a) (sec a - tan a) = 1   So, sec a - tan a = (2/5) ...........(II)   On adding equations (I) and (II), we get;   2 sec a = (5/2) + (2/5) = (25 + 4)/10 = (29/10)   Or, sec a = (29/20)   So, cos a = [1/(sec a)] = (20/29)   So, sin a = √[1 - (20/29)²] = √(441/841) = (21/29)   Hence, sin a = (21/29)

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