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The value of $\tan 67 \frac{1^{\circ}}{2}+\cot 67 \frac{1^{\circ}}{2}$ is
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Verified Answer
The correct answer is:
$2 \sqrt{2}$
Now, $\tan 67 \frac{1 \circ}{2}+\cot 67 \frac{1}{2} \circ$
$$
\begin{aligned}
&=\tan \left(90^{\circ}-22 \frac{1}{2}^{\circ}\right)+\cot \left(90^{\circ}-22 \frac{1}{2}^{\circ}\right) \\
&=\tan 22 \frac{1}{2}^{\circ}+\cot 22 \frac{1}{2} \circ \\
&=\sqrt{2}-1+\sqrt{2}+1 \\
&=2 \sqrt{2}
\end{aligned}
$$
$$
\begin{aligned}
&=\tan \left(90^{\circ}-22 \frac{1}{2}^{\circ}\right)+\cot \left(90^{\circ}-22 \frac{1}{2}^{\circ}\right) \\
&=\tan 22 \frac{1}{2}^{\circ}+\cot 22 \frac{1}{2} \circ \\
&=\sqrt{2}-1+\sqrt{2}+1 \\
&=2 \sqrt{2}
\end{aligned}
$$
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