Consider the expression (e^x)- In(cos²(x)) + ln(1+ (tan^2)(x)) and then simplify it into a single term

To simplify the expression:

\[
e^x - \ln(\cos^2(x)) + \ln\left(1 + \tan^2(x)\right)
\]

we can proceed with the following steps:

### Step 1: Use Trigonometric Identities
Recall the trigonometric identity:
\[
1 + \tan^2(x) = \sec^2(x)
\]
Thus, we can rewrite the expression as:
\[
e^x - \ln(\cos^2(x)) + \ln(\sec^2(x))
\]

### Step 2: Simplify Logarithmic Terms
Using the properties of logarithms:
- \(\ln(\sec^2(x)) = \ln\left(\frac{1}{\cos^2(x)}\right) = -\ln(\cos^2(x))\)

So, the expression becomes:
\[
e^x - \ln(\cos^2(x)) - (-\ln(\cos^2(x)))
\]

### Step 

Consider the expression (e^x) - ln(cos²(x)) + ln(1 + (tan^2)(x)) and then simplify it into a single term.

Simplify the expression (e^x) - ln(cos²(x)) + ln(1 + tan²(x)) using logarithmic properties and trigonometric identities. This solution covers exponential, logarithmic, and trigonometric functions, suitable for Grade 12 or college-level calculus.

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