(1)/(tan ^2)(8^(circ))=ldots

To solve the expression \( \frac{1}{\tan ^{2}\left(8^{\circ}\right)} \), we can use the trigonometric identity that relates tangent and secant:<br /><br />\[ \frac{1}{\tan^2(x)} = \sec^2(x) \]<br /><br />Here, \( x = 8^\circ \). Therefore,<br /><br />\[ \frac{1}{\tan^2(8^\circ)} = \sec^2(8^\circ) \]<br /><br />So, the final answer is:<br /><br />\[ \sec^2(8^\circ) \]