Trigonometric Identities Question 324
Question: $ \tan ( \frac{\pi }{4}+\theta )-\tan ( \frac{\pi }{4}-\theta )= $
Options:
A) $ 2\tan 2\theta $
B) $ 2\cot 2\theta $
C) $ \tan 2\theta $
D) $ \cot 2\theta $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \tan ( \frac{\pi }{4}+\theta )-\tan ( \frac{\pi }{4}-\theta )=\frac{1+\tan \theta }{1-\tan \theta }-\frac{1-\tan \theta }{1+\tan \theta } $ $ =\frac{4\tan \theta }{1-{{\tan }^{2}}\theta }=2( \frac{2\tan \theta }{1-{{\tan }^{2}}\theta } )=2\tan 2\theta $ .
BETA
