Trigonometric Identities Question 49
Question: Let A, B and C are the angles of a plain triangle and $ \tan \frac{A}{2}=\frac{1}{3},\tan \frac{B}{2}=\frac{2}{3} $ . Then $ \tan \frac{C}{2} $ is equal to
[Orissa JEE 2003]
Options:
A) 7/9
B) 2/9
C) 1/3
D) 2/3
Show Answer
Answer:
Correct Answer: A
Solution:
$ A+B+C=\pi $
$ \therefore ,\tan ( \frac{A+B}{2} )=\tan ( \frac{\pi }{2}-\frac{C}{2} ) $
Þ $ \frac{\tan \frac{A}{2}+\tan \frac{B}{2}}{1-\tan \frac{A}{2}.\tan \frac{B}{2}}=\cot \frac{C}{2}\Rightarrow \frac{\frac{1}{3}+\frac{2}{3}}{1-\frac{1}{3}.\frac{2}{3}}=\frac{9}{7}=\cot \frac{C}{2} $ \ $ \tan \frac{C}{2}=\frac{7}{9} $ .
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