False

We know,

sin θ increases when 0° ≤ θ ≤ 90°

cos θ decreases when 0° ≤ θ ≤ 90°

And (sin 80°-cos 80°) = (increasing value-decreasing value) which is always equal to a positive value.

∴ (sin 80°-cos 80°) > 0, which is positive (not negative).