What is (2sinθ − 3cosθ)/(2sinθ + 3cosθ)?

Think it through first, then pick an option.

Answer and explanation

Correct answer: b −5/13

Divide by cosθ: (2tanθ − 3)/(2tanθ + 3) = (4/3 − 3)/(4/3 + 3) = (−5/3)/(13/3) = −5/13.

Why the other options are wrong

a 1/7: 1/7 comes from taking sinθ = 2 and cosθ = 1; but tanθ = 2/3 means sinθ : cosθ = 2 : 3, so (4 − 9)/(4 + 9) = −5/13.
c −1/5: −1/5 is not a step of the working; it is a different quantity from the one asked for.
d 0: 0 would need the numerator to be zero, that is tanθ = 3/2; here it is 2/3.