An Identity Is a Promise for Every Input

You'll learnto tell an identity (true for every input) from an equation (true for only some).

Two expressions that agree at every angle. That standard is why no pile of examples proves an identity and why a single angle can destroy one. Watch the invented rules die on one input, watch the real ones come off the unit circle, and watch a division throw away half an answer.

8 STEPS · 6 QUICK CHECKS · PYTHAGOREAN · SUM · DOUBLE ANGLE · FACTOR NEVER DIVIDE · v2

one input can kill an identity

Before you start

What you're looking at

The unit-circle identity sin²θ + cos²θ = 1 shown geometrically, beside an equation to solve.

The question

Does this claim hold for every legal input, or only for particular ones?

Watch for

One counterexample killing an identity, while no pile of examples can prove one.

Step 1 / 8