Accuracy policy

“Verified” on this site means: the two sides were evaluated at up to 800 randomly sampled angles and agreed to within 1e-9 relative tolerance. It does not mean a proof was machine-checked.

What is guaranteed

• No identity is published without passing that check in the build. A failing record stops the whole build — there is no "known failing" list.
• The test itself is tested: each record is also run against a deliberately wrong right-hand side and must fail. That catches a checker that always says yes.
• Conditional formulas state their interval. The half-angle roots are the example:cos(x/2) = +√((1 + cos x)/2) is false outside −180° < x < 180°, and the build verifies that it really does fail outside.
• Triangle relations are sampled over real triangles (A + B + C = 180°, sides from the sine rule) and must fail against six independent random numbers.

What is not guaranteed

• Sampling is not proof. The written proofs on the proof pages carry the mathematical argument; the sampling catches transcription errors in the data.
• Curriculum coverage is a judgement. Which identities a course expects is decided by the syllabus, not by this site. For exam decisions use your teacher's list.
• Domain conventions. Angles are radians; functions are undefined at the usual points. The tool skips undefined points instead of guessing a value.

Reporting an error

This site publishes no mailbox yet, and it will not print an address that does not receive mail. Until one is announced here, the reliable route is the verifier: paste the two sides, and the page shows the angle where the claim breaks — that is the information a correction needs.

Data version 2026.09.26-1 · sources checked 2026-09-26 ·published data