Find the value of :
`cos^(2)60^(@)+sin^(2)30^(@)`

Answer

To find the value of \( \cos^2 60^\circ + \sin^2 30^\circ \), we can follow these steps:

### Step 1: Identify the trigonometric values
We know the values of the trigonometric functions for the angles involved:
- \( \cos 60^\circ = \frac{1}{2} \)
- \( \sin 30^\circ = \frac{1}{2} \)

### Step 2: Substitute the values into the expression
Now, we substitute these values into the expression:
\[ \cos^2 60^\circ + \sin^2 30^\circ = \left(\frac{1}{2}\right)^2 + \left(\frac{1}{2}\right)^2 \]

### Step 3: Calculate the squares
Next, we calculate the squares:
\[ \left(\frac{1}{2}\right)^2 = \frac{1}{4} \]
Thus, we have:
\[ \cos^2 60^\circ + \sin^2 30^\circ = \frac{1}{4} + \frac{1}{4} \]

### Step 4: Add the fractions
Now, we add the two fractions:
\[ \frac{1}{4} + \frac{1}{4} = \frac{2}{4} \]

### Step 5: Simplify the result
Finally, we simplify \( \frac{2}{4} \):
\[ \frac{2}{4} = \frac{1}{2} \]

### Final Answer
Therefore, the value of \( \cos^2 60^\circ + \sin^2 30^\circ \) is:
\[ \frac{1}{2} \]

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