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    Question

    If sec a + tan a = 4, find the value of sin a. 

    A 15/17 Correct Answer Incorrect Answer
    B 8/17 Correct Answer Incorrect Answer
    C 17/8 Correct Answer Incorrect Answer
    D 8/15 Correct Answer Incorrect Answer

    Solution

    Given, sec a + tan a = 4 ..............(I)   We know that, sec² a - tan² a = 1   Or, (sec a + tan a) (sec a - tan a) = 1   So, sec a - tan a = (1/4) ...........(II)   On adding equations (I) and (II), we get;   2 sec a = 4 + (1/4) = (17/4)   Or, sec a = (17/8)   So, cos a = [1/(sec a)] = (8/17)   So, sin a = √[1 - (8/17)²] = √(225/289) = (15/17)   Hence, sin a = (15/17) 

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