Question

If $\tan \Theta =2-\sqrt{3}$,then $\tan ({90}^{\circ }-\Theta )$ is equl to

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

Answer 1

Answer: (A)

$2+\sqrt{3}$

$\tan \theta =2-\sqrt{3}\tan (90-\theta )=\cot \theta =\frac{1}{2-\sqrt{3}}$
$=\frac{1}{2-\sqrt{3}}\times \frac{2+\sqrt{3}}{2+\sqrt{3}}=\frac{2+\sqrt{3}}{4-3}=\frac{2+\sqrt{3}}{1}=2+\sqrt{3}$