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Problem 10 - Entrance Test

If 4 tan θ = 3, then (4 sin θ - cos θ) / (4 sin θ + cos θ) is equal to:

Correct: C

Given 4 tan θ = 3, which implies tan θ = 3/4. To simplify the expression (4 sin θ - cos θ) / (4 sin θ + cos θ), divide both the numerator and the denominator by cos θ: = ((4 sin θ / cos θ) - (cos θ / cos θ)) / ((4 sin θ / cos θ) + (cos θ / cos θ)) = (4 tan θ - 1) / (4 tan θ + 1) Now, substitute tan θ = 3/4: = (4 * (3/4) - 1) / (4 * (3/4) + 1) = (3 - 1) / (3 + 1) = 2 / 4 = 1/2.