Trigonometric Identities Question 234
Question: The expression $ {{( \frac{\cos A+\cos B}{\sin A-\sin B} )}^{n}}+( \frac{\sin A+\sin B}{\cos A-\cos B} )= $
Options:
A) $ 2{{\cot }^{n}}( \frac{A-B}{2} ) $ if n is even
B) 0 if n is even
C) $ 2{{\cot }^{n}}( \frac{A-B}{2} ) $ if n is odd
D) 3 if n is odd
Show Answer
Answer:
Correct Answer: A
Solution:
The given expression $ ={{( \frac{2\cos ( \frac{A+B}{2} )\cos ( \frac{A-B}{2} )}{2\cos ( \frac{A+B}{2} )\sin ( \frac{A-B}{2} )} )}^{n}} $ $ +{{( \frac{2sin( \frac{A+B}{2} )\cos ( \frac{A-B}{2} )}{2sin( \frac{A+B}{2} )\sin ( \frac{B-A}{2} )} )}^{n}} $ $ ={{\cot }^{n}}( \frac{A-B}{2} )+{{(-1)}^{n}}{{\cot }^{n}}( \frac{A-B}{2} ) $
BETA
