Answer:
OPTION B: [tex]$ \frac{-2\sqrt{5}}{5} $[/tex]
Step-by-step explanation:
Given [tex]$ cot \theta = -\frac{\sqrt{5}}{2} $[/tex]
We know that, [tex]$ \frac{1}{cot \theta} = tan \theta $[/tex]
[tex]$ \implies tan \theta = \frac{1}{-\frac{\sqrt{5}}{2}} $[/tex]
[tex]$ = -\frac{2}{\sqrt{5}} $[/tex]
Multiplying and dividing by [tex]$ \sqrt{5} $[/tex], we get:
[tex]$ tan \theta = - \frac{2 \sqrt{5}}{\sqrt{5}\times \sqrt{5}}} $[/tex]
[tex]$ \implies tan \theta = -\frac{2\sqrt{5}}{5} $[/tex]
Hence, OPTION B is the answer.
