KCET · Maths · Trigonometric Ratios & Identities
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 & Solution
Correct Answer
(C) \(2 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
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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