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    Question

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

    A 3/5 Correct Answer Incorrect Answer
    B 4/5 Correct Answer Incorrect Answer
    C 3/4 Correct Answer Incorrect Answer
    D 5/3 Correct Answer Incorrect Answer

    Solution

    Given, sec a + tan a = 2 ..............(I)Ā  We know that, secĀ² a - tanĀ² a = 1Ā  Or, (sec a + tan a) (sec a - tan a) = 1Ā  Ā So, sec a - tan a = (1/2) ...........(II)Ā  Ā On adding equations (I) and (II), we get;Ā  Ā 2 sec a = 2 + (1/2) = (5/2)Ā  Ā Or, sec a = (5/4)Ā  Ā So, cos a = [1/(sec a)] = (4/5)Ā  Ā So, sin a = āˆš[1 - (4/5)Ā²] = āˆš(9/25) = (3/5)Ā  Ā Hence, sin a = (3/5)Ā 

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