Question

The value of $\frac{\tan {225}^{\circ }-\cot {81}^{\circ }\cot {69}^{\circ }}{\cot {261}^{\circ }+\tan {21}^{\circ }}$ is

• A. $1$
• B. $\sqrt{3}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is B $\sqrt{3}$

$\frac{\tan {225}^{\circ }-\cot {81}^{\circ }\cot {69}^{\circ }}{\cot {261}^{\circ }+\tan {21}^{\circ }}$
We know that,
$\tan {225}^{\circ }=1,\cot {261}^{\circ }=\cot {81}^{\circ },\tan {21}^{\circ }=\cot {69}^{\circ }$
substituting this values in the given expresssion,
$\frac{\tan {225}^{\circ }-\cot {81}^{\circ }\cot {69}^{\circ }}{\cot {261}^{\circ }+\tan {21}^{\circ }}=\frac{1-\cot {81}^{\circ }\cot {69}^{\circ }}{\cot {81}^{\circ }+\cot {69}^{\circ }}=-\left(\frac{\cot {81}^{\circ }\cot {69}^{\circ }-1}{\cot {81}^{\circ }+\cot {69}^{\circ }}\right)=-\cot ({81}^{\circ }+{69}^{\circ })=-\cot {150}^{\circ }=\cot {30}^{\circ }=\sqrt{3}$