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 will follow these steps:

### Step 1: Find \( \cos 60^\circ \)
We know that:
\[ \cos 60^\circ = \frac{1}{2} \]

### Step 2: Calculate \( \cos^2 60^\circ \)
Now, we square the value of \( \cos 60^\circ \):
\[ \cos^2 60^\circ = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \]

### Step 3: Find \( \sin 30^\circ \)
Next, we know that:
\[ \sin 30^\circ = \frac{1}{2} \]

### Step 4: Calculate \( \sin^2 30^\circ \)
Now, we square the value of \( \sin 30^\circ \):
\[ \sin^2 30^\circ = \left(\frac{1}{2}\right)^2 = \frac{1}{4} \]

### Step 5: Add \( \cos^2 60^\circ \) and \( \sin^2 30^\circ \)
Now, we add the two squared values together:
\[ \cos^2 60^\circ + \sin^2 30^\circ = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \]

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

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