Question

The value of $\tan 67\frac{1^{\circ }}{2}+\cot 67\frac{1^{\circ }}{2}$ is

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

Answer 1

Answer: (C)

Now, $\tan 67{\frac{1}{2}}^{\circ }+\cot 67{\frac{1}{2}}^{\circ }$
$=\tan \left(90^{\circ }-22{\frac{1}{2}}^{\circ }\right)+\cot \left(90^{\circ }-22{\frac{1}{2}}^{\circ }\right)$
$=\tan 22{\frac{1}{2}}^{\circ }+\cot 22{\frac{1}{2}}^{\circ }$
$=\sqrt{2}-1+\sqrt{2}+1$
$=2\sqrt{2}$