Trigonometric Identities Question 190
Question: If $ \tan \beta =\cos \theta \tan \alpha , $ then $ {{\tan }^{2}}\frac{\theta }{2}= $
Options:
A) $ \frac{\sin (\alpha +\beta )}{\sin (\alpha -\beta )} $
B) $ \frac{\cos (\alpha -\beta )}{\cos (\alpha +\beta )} $
C) $ \frac{\sin (\alpha -\beta )}{\sin (\alpha +\beta )} $
D) $ \frac{\cos (\alpha +\beta )}{\cos (\alpha -\beta )} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ {{\tan }^{2}}\frac{\theta }{2}=\frac{1-\cos \theta }{1+\cos \theta }=\frac{\tan \alpha -\tan \beta }{\tan \alpha +\tan \beta }=\frac{\sin (\alpha -\beta )}{\sin (\alpha +\beta )} $ .
BETA
