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    Question

    If sec A + tan A = 3 then the value of cot A

    is:
    A 4/3 Correct Answer Incorrect Answer
    B 2/3 Correct Answer Incorrect Answer
    C 3/4 Correct Answer Incorrect Answer
    D 1/3 Correct Answer Incorrect Answer

    Solution

    sec A + tan A = 3 ... (1) (sec A + tan A)*(sec A - tan A)/(sec A - tan A) = 11/2 ⇒ (sec2A - tan2A) /(sec A - tan A ) = 11/2 ⇒ 1/(sec A – tan A) = 3 (Since sec2A - tan2A = 1) ⇒ sec A - tan A = 1/3 ... (2) From (1) - (2), we get, 2 tan A = 3 -1/3 = 8/3 ⇒ tan A = 4/3 Therefore, cot A = 1/tan A = 3/4

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