If `cos theta = (1)/(sqrt2) " then " theta`

Options

A. `30^@`
B. `45^@`
C. `60^@`
D. `90^@`

Answer

To solve the problem where \( \cos \theta = \frac{1}{\sqrt{2}} \), we can follow these steps:

### Step 1: Identify the value of \( \cos \theta \)
We start with the equation given in the problem:
\[ \cos \theta = \frac{1}{\sqrt{2}} \]

### Step 2: Recall the trigonometric values
We need to recall the standard values of cosine for common angles. The cosine of 45 degrees is:
\[ \cos 45^\circ = \frac{1}{\sqrt{2}} \]

### Step 3: Set the angles equal
Since we have established that:
\[ \cos \theta = \cos 45^\circ \]
This implies that:
\[ \theta = 45^\circ \]

### Step 4: Conclusion
Thus, the value of \( \theta \) is:
\[ \theta = 45^\circ \]

### Final Answer
The answer is \( \theta = 45^\circ \) (Option B).

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