If `ptan45^@.cos60^@=sin60^@cot60^@`, then p is equal to

Options

A. 1
B. 0
C. `sqrt3`
D. `1/sqrt2`

Answer

To solve the equation \( p \tan 45^\circ \cdot \cos 60^\circ = \sin 60^\circ \cdot \cot 60^\circ \), we will follow these steps:

### Step 1: Substitute the known values
We know the following trigonometric values:
- \( \tan 45^\circ = 1 \)
- \( \cos 60^\circ = \frac{1}{2} \)
- \( \sin 60^\circ = \frac{\sqrt{3}}{2} \)
- \( \cot 60^\circ = \frac{1}{\sqrt{3}} \)

Substituting these values into the equation gives:
\[ p \cdot 1 \cdot \frac{1}{2} = \frac{\sqrt{3}}{2} \cdot \frac{1}{\sqrt{3}} \]

### Step 2: Simplify the right-hand side
Now simplify the right-hand side:
\[ \frac{\sqrt{3}}{2} \cdot \frac{1}{\sqrt{3}} = \frac{1}{2} \]

### Step 3: Set up the equation
Now we have:
\[ p \cdot \frac{1}{2} = \frac{1}{2} \]

### Step 4: Solve for \( p \)
To isolate \( p \), multiply both sides by 2:
\[ p = 1 \]

### Final Answer
Thus, the value of \( p \) is:
\[ \boxed{1} \]