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.