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    Question

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

    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)┬а We know that, sec┬▓ a - tan┬▓ a = 1┬а Or, (sec a + tan a) (sec a - tan a) = 1┬а ┬аSo, sec a - tan a = (1/2) ...........(II)┬а ┬аOn adding equations (I) and (II), we get;┬а ┬а2 sec a = 2 + (1/2) = (5/2)┬а ┬аOr, sec a = (5/4)┬а ┬аSo, cos a = [1/(sec a)] = (4/5)┬а ┬аSo, sin a = тИЪ[1 - (4/5)┬▓] = тИЪ(9/25) = (3/5)┬а ┬аHence, sin a = (3/5)┬а

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