Verified answer

Assuming cos2(α) is cos^2(a), the anything squared is always positive. Therefore, the only part that affects the answer is which quadrants cot(α)<0 in. Use a reference angle in each quadrant.

cot(α)=adj/opp

Quadrant I

cot(α)=positive/positive

Not less than 0

Quadrant II

cot(α)=negative/positive

Is less than 0

Quadrant III

cot(α)=negative/negative

Not less than 0 (the negatives will cancel out and form a positive)

Quadrant IV

cot(α)=positive/negative

Is less than 0

Your answer would be that quadrants II and IV satisfy the conditions cot(α)<0 and (even though it is useless to have) cos^2(α)>0.