For an acute angle θ, three of these four expressions are equal to one another. Which is the odd one out?

Splitting the first expression gives 1/cosθ − sinθ/cosθ = secθ − tanθ, so those two agree. Multiplying the second above and below by (1 − sinθ) turns it into cosθ(1 − sinθ)/(1 − si$n^2$θ) = cosθ(1 − sinθ)/co$s^2$θ = (1 − sinθ)/cosθ, so it joins them. The odd one out is cosθ/(1 − sinθ), which by the same rationalising step equals (1 + sinθ)/cosθ = secθ + tanθ — the conjugate, hence the reciprocal, of the other three. Check at θ = 30°: the three matching values are 0.5774 while the odd one is 1.7321.