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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 √3/2. Correct Answer Incorrect Answer
    B 2 /√3. Correct Answer Incorrect Answer
    C 1 /√3. Correct Answer Incorrect Answer
    D √3. Correct Answer Incorrect Answer

    Solution

      tan(t) + cot(t) = 1, sin(t)/cos(t) + cos(t) /sin(t) = 1   sin²(t) + cos²(t) = sin(t) cos(t) sin(t) cos(t)= 1            … (1) Squaring sin(t) + cos(t), (sin(t) + cos(t)) ² = 1 + 2 sin(t) cos(t)   = 1 + 2 × 1 = 3   sin(t) + cos(t) = √3 Thus, 1/ sin(t) + cos(t) = 1 /√3 = =1 /√3.

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