I will write it again...... it's Tan(45)square/2+Tan(30)

Let's break down the expression step by step:

\[
\frac{\tan^2(45^\circ)}{2} + \tan(30^\circ)
\]

### Step 1: Calculate \(\tan(45^\circ)\)
\[
\tan(45^\circ) = 1
\]

So, \(\tan^2(45^\circ) = 1^2 = 1\).

### Step 2: Calculate \(\tan(30^\circ)\)
\[
\tan(30^\circ) = \frac{1}{\sqrt{3}} \approx 0.577
\]

### Step 3: Substitute values into the expression
Now the expression becomes:
\[
\frac{1}{2} + \frac{1}{\sqrt{3}}
\]

### Step 4: Simplify
To simplify further, let's express everything with a common denominator.

\[
\frac{1}{2} + \frac{1}{\sqrt{3}} \approx 0.5 + 0.577 = 1.077
\]

The approximate value of the expression is:
\[
\boxed{1.077}
\]

Let me know if you'd like more details or have questions. Here are some related problems to explore:

1. What is \(\tan(60^\circ)\)?
2. How do you find the exact value of \(\tan(30^\circ)\)?
3. What is \(\frac{\tan^2(60^\circ)}{2} + \tan(45^\circ)\)?
4. How does \(\tan^2(45^\circ)\) relate to other trigonometric identities?
5. What is \(\frac{\tan^2(30^\circ)}{2} + \tan(45^\circ)\)?

**Tip**: When working with trigonometric functions, it’s helpful to remember the exact values for angles like 30°, 45°, and 60°.

Step-by-step solution for simplifying the trigonometric expression Tan(45°)²/2 + Tan(30°). Learn how to use exact trigonometric values and simplify the result to approximately 1.077. This problem explores key trigonometric concepts and identities, suitable for students in Grades 9-10.

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