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Question
sin θ = 0.5 implies tan θ + cot θ is equal to:
Options
\[2 : \sqrt{3}\]
\[\sqrt{3} : 4\]
\[4 : \sqrt{3}\]
\[\sqrt{3} : 2\]
MCQ
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Solution
\[\boldsymbol{4 : \sqrt{3}}\]
Given,
\[\Rightarrow \sin \theta = 0.5\]
\[\Rightarrow \sin \theta = \frac{5}{10}\]
\[\Rightarrow \sin \theta = \frac{1}{2}\]
\[\Rightarrow \sin \theta = \sin 30^\circ\]
\[\Rightarrow \theta = 30^\circ.\]
Substituting value of \[\theta\] in \[\tan \theta + \cot \theta\], we get:
\[\Rightarrow \tan \theta + \cot \theta\]
\[\Rightarrow \tan 30^\circ + \cot 30^\circ\]
\[\Rightarrow \frac{1}{\sqrt{3}} + \sqrt{3}\]
\[\Rightarrow \frac{1 + 3}{\sqrt{3}}\]
\[\Rightarrow \frac{4}{\sqrt{3}}\]
\[\Rightarrow 4 : \sqrt{3}\]
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