Trigonometric Identities Question 291
Question: If $ \tan \frac{A}{2}=\frac{3}{2}, $ then $ \frac{1+\cos A}{1-\cos A}= $
Options:
A) $ -5 $
B) $ 5 $
C) $ 9/4 $
D) $ 4/9 $
Show Answer
Answer:
Correct Answer: D
Solution:
Given that $ \tan \frac{A}{2}=\frac{3}{2} $ . $ \frac{1+\cos A}{1-\cos A}=\frac{2{{\cos }^{2}}\frac{A}{2}}{2{{\sin }^{2}}\frac{A}{2}}={{\cot }^{2}}\frac{A}{2}={{( \frac{2}{3} )}^{2}}=\frac{4}{9} $ .
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