A) \[2{{\cot }^{n}}\left( \frac{A-B}{2} \right)\] if n is even
B) 0 if n is even
C) \[2{{\cot }^{n}}\left( \frac{A-B}{2} \right)\]if n is odd
D) 3 if n is odd
Correct Answer: A
Solution :
The given expression \[={{\left( \frac{2\cos \left( \frac{A+B}{2} \right)\cos \left( \frac{A-B}{2} \right)}{2\cos \left( \frac{A+B}{2} \right)\sin \left( \frac{A-B}{2} \right)} \right)}^{n}}\]\[+{{\left( \frac{2sin\left( \frac{A+B}{2} \right)\cos \left( \frac{A-B}{2} \right)}{2sin\left( \frac{A+B}{2} \right)\sin \left( \frac{B-A}{2} \right)} \right)}^{n}}\] \[={{\cot }^{n}}\left( \frac{A-B}{2} \right)+{{(-1)}^{n}}{{\cot }^{n}}\left( \frac{A-B}{2} \right)\]You need to login to perform this action.
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