Question

sin θ = 0.5 implies tan θ + cot θ is equal to:

विकल्प

• \[2 : \sqrt{3}\]

• \[\sqrt{3} : 4\]

• \[4 : \sqrt{3}\]

• \[\sqrt{3} : 2\]

Answer 1

\[\boldsymbol{4 : \sqrt{3}}\]

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:

\[\Rightarrow \tan \theta + \cot \theta\]

\[\Rightarrow \tan 30^\circ + \cot 30^\circ\]

\[\Rightarrow \frac{1}{\sqrt{3}} + \sqrt{3}\]

\[\Rightarrow \frac{1 + 3}{\sqrt{3}}\]

\[\Rightarrow \frac{4}{\sqrt{3}}\]

\[\Rightarrow 4 : \sqrt{3}\]