We know that the above expression is equivalent to $\cot \left( A-B \right)$ . Therefore, the
Answer is option (a) $\cot \left( A-B \right)$
Note: It is preferred to keep the expression as neat as possible by eliminating all the removable terms as the larger is the number of terms in your expression more is the probability of making a mistake. In trigonometry, it is often seen that many formulas lead to the same answer. However, the complexity of the question varies with the selection of the formula. The wiser the selection of formula, the easier the question will be to solve.