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    Question

    Find the value of tan(75┬░) using the identity for

    tan(A+B).
    A 2 + тИЪ3 Correct Answer Incorrect Answer
    B 2 - тИЪ3 Correct Answer Incorrect Answer
    C 3 + тИЪ2 Correct Answer Incorrect Answer
    D тИЪ3 - 1 Correct Answer Incorrect Answer

    Solution

    We know tan(75┬░) = tan(45┬░ + 30┬░). Using the formula tan(A+B) = (tanA + tanB) / (1 - tanA * tanB), tan(75┬░) = (tan(45┬░) + tan(30┬░)) / (1 - tan(45┬░) * tan(30┬░)). = (1 + 1/тИЪ3) / (1 - 1 * 1/тИЪ3) = (тИЪ3 + 1) / (тИЪ3 - 1). Multiplying numerator and denominator by (тИЪ3 + 1), = [(тИЪ3 + 1)┬▓] / [(тИЪ3)┬▓ - (1)┬▓] = (3 + 2тИЪ3 + 1) / (3 - 1) = (4 + 2тИЪ3) / 2 = 2 + тИЪ3.

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