Trigonometric Identities Question 289
Question: If $ \sec \theta =1\frac{1}{4} $ , then $ \tan \frac{\theta }{2}= $
Options:
A) $ \frac{1}{3} $
B) $ \frac{3}{4} $
C) $ \frac{1}{4} $
D) $ \frac{5}{4} $
Show Answer
Answer:
Correct Answer: A
Solution:
Given that $ \sec \theta =\frac{5}{4} $ $ \sec \theta =\frac{1+{{\tan }^{2}}(\theta /2)}{1-{{\tan }^{2}}(\theta /2)}\Rightarrow \frac{5}{4}=\frac{1+{{\tan }^{2}}(\theta /2)}{1-{{\tan }^{2}}(\theta /2)} $
Þ $ 5-5{{\tan }^{2}}(\theta /2)=4+4{{\tan }^{2}}(\theta /2) $
Þ $ 9{{\tan }^{2}}(\theta /2)=1,\Rightarrow \tan (\theta /2)=\frac{1}{3} $ .
BETA
