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

KCETKCET 2008Trigonometric Functions

Solution:

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