The area of the circle and the area of a regular polygon of `n` sides and of perimeter equal to that of the circle are in the ratio of `tan(pi/n):pi/n` (b) `cos(pi/n):pi/n` `sinpi/n :pi/n` (d) `cot(pi/n):pi/n`

Explanation

To find the ratio of the area of a circle to the area of a regular polygon with \( n \) sides and the same perimeter as the circle, we can follow these steps:

### Step 1: Define the radius of the circle
Let the radius of the circle be \( r \).

### Step 2: Calculate the perimeter of the circle
The perimeter (circumference) of the circle is given by:
\[
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