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Question: Answered & Verified by Expert
The value of $\tan 67 \frac{1^{\circ}}{2}+\cot 67 \frac{1^{\circ}}{2}$ is
MathematicsTrigonometric Ratios & IdentitiesKCETKCET 2008
Options:
  • A $\sqrt{2}$
  • B $3 \sqrt{2}$
  • C $2 \sqrt{2}$
  • D $2-\sqrt{2}$
Solution:
2890 Upvotes Verified Answer
The correct answer is: $2 \sqrt{2}$
Now, $\tan 67 \frac{1 \circ}{2}+\cot 67 \frac{1}{2} \circ$
$$
\begin{aligned}
&=\tan \left(90^{\circ}-22 \frac{1}{2}^{\circ}\right)+\cot \left(90^{\circ}-22 \frac{1}{2}^{\circ}\right) \\
&=\tan 22 \frac{1}{2}^{\circ}+\cot 22 \frac{1}{2} \circ \\
&=\sqrt{2}-1+\sqrt{2}+1 \\
&=2 \sqrt{2}
\end{aligned}
$$

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