Trigonometric Identities Question 44
Question: If $ \tan A-\tan B=x $ and $ \cot B-\cot A=y, $ then $ \cot (A-B)= $
Options:
A) $ \frac{1}{x}+y $
B) $ \frac{1}{xy} $
C) $ \frac{1}{x}-\frac{1}{y} $
D) $ \frac{1}{x}+\frac{1}{y} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \cot ,(A-B)=\frac{1}{\tan ,(A-B)}=\frac{1+\tan A\tan B}{\tan A-\tan B} $ $ =\frac{1}{\tan A-\tan B}+\frac{\tan A\tan B}{\tan A-\tan B}=\frac{1}{x}+\frac{1}{y} $ .
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