Step 1 — State the fundamental identity for direction cosines.

If $l$, $m$, $n$ are the direction cosines of a line, they must always satisfy

$$l^2 + m^2 + n^2 = 1$$

Step 2 — Test the Assertion.

Substituting $l = m = n = 1$:

$$1^2 + 1^2 + 1^2 = 3 \ne 1$$

The identity fails, so $\langle 1, 1, 1\rangle$ cannot be a set of direction cosines.

Assertion (A) is FALSE.

(Note: $\langle 1, 1, 1\rangle$ is a valid set of direction ratios, but not direction cosines. The corresponding direction cosines would be $\left\langle \frac{1}{\sqrt3}, \frac{1}{\sqrt3}, \frac{1}{\sqrt3}\right\rangle$.)

Step 3 — Test the Reason.

$$\cos 0 = 1$$

This is a correct statement about the cosine function.

Reason (R) is TRUE.

Step 4 — Conclusion.

Assertion is false, Reason is true.

$$\boxed{\text{Option (D)}}$$

Why R does not save A: a single direction cosine can indeed equal 1 (when the line is along that axis), but then the other two must be 0 so that the sum of squares stays 1. All three cannot be 1 simultaneously.