A) \[\frac{1}{3}\]
B) \[\frac{3}{4}\]
C) \[\frac{1}{4}\]
D) \[\frac{5}{4}\]
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 \[9{{\tan }^{2}}(\theta /2)=1\,\Rightarrow \tan (\theta /2)=\frac{1}{3}\].
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