How do you prove tan^2(x)+1+tan(x)sec(x)=1+sin(x)/co s^2(x)?

You are standing next to a really big circular lake. you want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! you decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400? m. what is the diameter dd of the lake?