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    Question

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

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

    Solution

    Given, sec a + tan a = 3 ..............(I)  We know that, sec² a - tan² a = 1  Or, (sec a + tan a) (sec a - tan a) = 1  So, sec a - tan a = (1/3) ...........(II)  On adding equations (I) and (II), we get;  2 sec a = 3 + (1/3) = (10/3)  Or, sec a = (5/3)  So, cos a = [1/(sec a)] = (3/5)  So, sin a = √[1 - (3/5)²] = √(16/25) = (4/5)  Hence, sin a = (4/5) 

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