Solve ${\sin }^{2}x+{\cos }^{2}x=1$

Step-by-step solution

1. Step 1 · Unit circle equation
   $$x^2+y^2=1$$

   Every point on a circle of radius 1 satisfies this.

2. Step 2 · Definition on the unit circle
   $$x=\cos \theta ,y=\sin \theta$$

   The coordinates of the point at angle θ are exactly cosine and sine.

3. Step 3 · Substitute
   $${\cos }^2\theta +{\sin }^2\theta =1$$

   The identity is the Pythagorean theorem written in trigonometric form.