• question_answer ${{\left( \frac{\cos A+\cos B}{\sin A-\sin B} \right)}^{n}}+{{\left( \frac{\sin A+\sin B}{\cos A-\cos B} \right)}^{n}}$(n even or odd) = A) $2{{\tan }^{n}}\frac{A-B}{2}$ B) $2{{\cot }^{n}}\frac{A-B}{2}$ C) $0$ D) None of these

The expression reduces to ${{\cot }^{n}}\frac{A-B}{2}+{{\cot }^{n}}\frac{B-A}{2}$ If n is even, answer is (b) and if n is odd answer is (c).