Question

If $\tan {15}^{\circ }=2-\sqrt{3},$ then the value of ${\cot }^2{75}^{\circ }$ is

• A. $7+\sqrt{3}$
• B. $7-2\sqrt{3}$
• C. $7-4\sqrt{3}$
• D. $7+4\sqrt{3}$

Answer 1

The correct option is C $7-4\sqrt{3}$

Given, $tan{15}^0=2-\sqrt{3}$
$\Rightarrow tan({90}^0-{75}^0)=2-\sqrt{3}$
$\Rightarrow cot{75}^0=2-\sqrt{3}$
$\Rightarrow co{t}^2{75}^0=4+3-4\sqrt{3}$
$\Rightarrow co{t}^2{75}^0=7-4\sqrt{3}$
Option C is correct.