Q75 / 180 · KCET 2008 · Mathematics
The value of $\tan 67 \frac{1^{\circ}}{2}+\cot 67 \frac{1^{\circ}}{2}$ is
- A$\sqrt{2}$
- B$3 \sqrt{2}$
- Correct answerC$2 \sqrt{2}$
- D$2-\sqrt{2}$
Solution
Now, $\tan 67 \frac{1 \circ}{2}+\cot 67 \frac{1}{2} \circ$
$$
\begin{aligned}
&=\tan \left(90^{\circ}-22 \frac{1}{2}^{\circ}\right)+\cot \left(90^{\circ}-22 \frac{1}{2}^{\circ}\right) \\
&=\tan 22 \frac{1}{2}^{\circ}+\cot 22 \frac{1}{2} \circ \\
&=\sqrt{2}-1+\sqrt{2}+1 \\
&=2 \sqrt{2}
\end{aligned}
$$
Hence, the correct answer is option: 'C'.