Trigonometric Identities Question 348
Question: If $ \tan A=2\tan B+\cot B, $ then $ 2\tan (A-B)= $
Options:
A) $ \tan B $
B) $ 2\tan B $
C) $ \cot B $
D) $ 2\cot B $
Show Answer
Answer:
Correct Answer: C
Solution:
$ 2\tan ,(A-B)=2,( \frac{\tan A-\tan B}{1+\tan A\tan B} ) $ $ =2\frac{(2\tan B+\cot B-\tan B)}{1+(2,\tan B+\cot B),\tan B}=2,\frac{\tan B+\cot B}{2,(1+{{\tan }^{2}}B)} $ $ =\frac{\cot B,({{\tan }^{2}}B+1)}{(1+{{\tan }^{2}}B)}=\cot B $ .
BETA
