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Fundamental trigonometric identity

Why cos⁡2θ+sin⁡2θ=1\cos^2\theta+\sin^2\theta=1
The endpoint on the unit circle is (cos⁡θ;sin⁡θ)(\cos\theta;\sin\theta). For coordinates on a circle r=1r=1, Pythagoras gives (cos⁡θ)2+(sin⁡θ)2=1.(\cos\theta)^2+(\sin\theta)^2=1. It is customary to write cos⁡2θ+sin⁡2θ=1\cos^2\theta+\sin^2\theta=1 for all θ\theta.
The identity does not depend on the quadrant: for every θ\theta the sum of squares is 11
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