False

cos² 23° - sin² 67° =(cos 23°+sin 67°)(cos 23°-sin 67°)

(∵(a²-b²) = (a+b)(a-b))

= [cos 23°+sin(90°-23°)] [cos 23°-sin(90°-23°)]

= (cos 23°+cos 23°)(cos 23°-cos 23°) (∵sin(90°-θ) = cos θ)

= (cos 23°+cos 23°).0

= 0, which is neither positive nor negative