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 $(\sin (t))^{2}$ .
Question Help:
Video
Message instructor
Submit Question

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The simplified expression is $\sec^{2} (t)$ .

Steps

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 $\sec^{2} (t)$ .