1. Identify the geometry and ligands

The complexes are: $\text{trans-}[Co(en)_2Cl_2]^+ \quad (A), \qquad \text{cis-}[Co(en)_2Cl_2]^+ \quad (B)$

Here, $en$ = ethylenediamine, which is a bidentate ligand. Since there are two $en$ ligands and two $Cl^-$ ligands, the coordination number is $6$, so the complex is octahedral.

2. Criterion for optical activity

A complex is optically active if it is chiral, i.e. it does not possess a plane of symmetry, center of symmetry, or improper axis of rotation.

3. Analyze the trans isomer $\text{(A)}$

For $\text{trans-}[Co(en)_2Cl_2]^+$ the two chloride ligands are opposite to each other.

This arrangement has sufficient symmetry (in particular, it possesses a symmetry element making it superimposable on its mirror image), so the trans isomer is achiral.

Hence, (A) is not optically active.

4. Analyze the cis isomer $\text{(B)}$

For $\text{cis-}[Co(en)_2Cl_2]^+$ the two chloride ligands are adjacent.

With two bidentate $en$ ligands arranged in the cis form, the complex can adopt a helical arrangement, giving rise to non-superimposable mirror images ($\Delta$ and $\Lambda$ forms).

Therefore, the cis isomer is chiral and can be optically active.

5. Evaluate the options

• A: both (A) and (B) can be optically active.
  False.
• B: both (A) and (B) can not be optically active.
  False.
• C: (A) can not be optically active, but (B) can be optically active.
  True.
• D: (A) can be optically active, but (B) can not be optically active.
  False.

Therefore, the correct option is: $\boxed{\text{C}}$

6. Comparison with stored answer

Stored correct answer = C. This matches the derived answer.