$$tan θ + 1/tanθ = 2$$
$$tan^2 θ + 1 = 2 tan θ$$
$$sec ^2 θ = 2 tan θ$$
$$hypotenuse^2 / adjacent side^2 = 2 opposite side / adjacent side$$
$$hypotenuse^2 / adjacent side = 2* opposite side$$
$$hypotenuse/adjacent side = 2* opposite side/adjacent side$$
$$1/cos θ = 2 sin θ$$
$$sin θ. cos θ = 1/2$$
We know that, when θ = 45 degrees, this relation will hold true.
Therefore, option C is the right answer.