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    Question

    If tan(t) + cot(t) = 1, then one of the values of the

    expression 1/[sin(t)+cos(t)] is.
    A тИЪ3/2. Correct Answer Incorrect Answer
    B 2 /тИЪ3. Correct Answer Incorrect Answer
    C 1 /тИЪ3. Correct Answer Incorrect Answer
    D тИЪ3. Correct Answer Incorrect Answer

    Solution

    ┬а tan(t) + cot(t) = 1, sin(t)/cos(t) + cos(t) /sin(t) = 1 ┬а sin┬▓(t) + cos┬▓(t) = sin(t) cos(t) sin(t) cos(t)= 1 ┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а тАж (1) Squaring sin(t) + cos(t), (sin(t) + cos(t)) ┬▓ = 1 + 2 sin(t) cos(t) ┬а = 1 + 2 ├Ч 1 = 3 ┬а sin(t) + cos(t) = тИЪ3 Thus, 1/ sin(t) + cos(t) = 1 /тИЪ3 = =1 /тИЪ3.

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