Question

If $\tan {15}^o=2-\sqrt{3}$, then the value of ${\cot }^2{75}^o$ 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 $7-4\sqrt{3}$

$\tan {15}^{\circ }=\tan ({90}^{\circ }-{75}^{\circ })=\cot {75}^{\circ }{\cot }^2{75}^{\circ }={\tan }^2{15}^{\circ }={(2-\sqrt{3})}^2=4-4\sqrt{3}+3=7-4\sqrt{3}$