If you add Cos²θ + Sin²θ does it equal 1? How do you prove it?

Yes, it does equal one.

There are a number of ways to do it. The easiest that I know of is to use a unit circle with center on the origin of a cartesian coordinate system. Draw a right triangle from the origin to any point on the unit circle. From the definition of sine and cosine, figure out the lengths of the sides. Use the Pythagorean theorem to prove that

sin^2(\theta) + cos^2(\theta)=1

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