The correct option is B Promised to be given a lighter sentence, the suspect cooperated with the police.
A participle is a form of a verb that ends with an -ed or -ing, like 'work', 'worked' and 'working'.
The given sentence must be re-written with a participle.
Option B: This sentence begins with a participle 'promised'. Also, it changes the conditional sentence into an assertive, simple one. Hence option B is correct.
Option A: 'Unless' also refers to condition, so the sentence has not been changed from conditional to assertive. Also, this sentence does not use any participle to change the conditional.
Option C: The words in the sentence have been changed; the suspect is not told to 'confess', but to 'cooperate'.
Hence options A and C are incorrect.
Option D is incorrect because the answer lies in B.