Simplify $\frac{\sin ^{2}(t)+\cos ^{2}(t)}{\cos ^{2}(t)}$ to an expression involving a single trig function with no fractions.
If needed, enter squared trigonometric expressions using the following notation. Example: Enter $\sin ^{2}(t)$ as $(\sin (t))^{2}$.
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Final Answer: The simplified expression is \(\boxed{\sec ^{2}(t)}\).
Step 1 ：The given expression is \(\frac{\sin ^{2}(t)+\cos ^{2}(t)}{\cos ^{2}(t)}\).
Step 2 ：We know that \(\sin ^{2}(t)+\cos ^{2}(t) = 1\) for all \(t\).
Step 3 ：So, we can simplify the expression to \(\frac{1}{\cos ^{2}(t)}\).
Step 4 ：This is equivalent to \(\sec ^{2}(t)\), where \(\sec (t)\) is the secant function, which is the reciprocal of the cosine function.
Step 5 ：So, the simplified expression is \(\sec ^{2}(t)\).
Step 6 ：Final Answer: The simplified expression is \(\boxed{\sec ^{2}(t)}\).
