The correct answer is: E. has been dieting/has lost
The sentence is in the present perfect continuous tense, which is used to talk about an action that started in the past and continues up to the present. In this case, the action is “dieting” and the time reference is “since Christmas”. The past participle of “diet” is “dieted”, so the correct verb form to use in the present perfect continuous tense is “has been dieting”. The past participle of “lose” is “lost”, so the correct verb form to use in the present perfect continuous tense is “has lost”.
The other options are incorrect because they do not use the correct tense. Option A, “was dieting/was losing”, is in the past simple tense, which is used to talk about an action that happened at a specific time in the past. Option B, “dieted/loses”, is in the simple past tense and the simple present tense, respectively. These tenses are not appropriate for this sentence because they do not express the idea that the action of dieting started in the past and continues up to the present. Option C, “diets/is losing”, is in the simple present tense and the present continuous tense, respectively. These tenses are also not appropriate for this sentence because they do not express the idea that the action of dieting started in the past. Option D, “is dieting/lost”, is in the present continuous tense and the past tense, respectively. These tenses are also not appropriate for this sentence because they do not express the idea that the action of dieting started in the past and continues up to the present.