The area of the circle and the area of a regular polygon of `n` sides and the perimeter of polygon 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 solve the problem, we need to find the ratio of the area of a circle to the area of a regular polygon with \( n \) sides, given that the perimeter of the polygon is equal to the perimeter of the circle.

### Step-by-Step Solution:

1. **Define the Perimeter of the Circle and Polygon:**
- The perimeter \( P \) of the circle is given by:
\[
P_{\text{circle}} = 2\pi r
...