True or False?

A real identity — half of them subtly broken. You guess; the verdict is checked, not assumed.

equations.identity · v1 · renderer math

1. cos(3x) = 4cos(x)^3 + 3cos(x) → False — the sign of 3 flipped; it should read cos(3x) = 4cos(x)^3 - 3cos(x) 2. sin(a + b) = sin(a)cos(b) + sin(a)sin(b) → False — a cos became a sin; it should read sin(a + b) = sin(a)cos(b) + cos(a)sin(b) 3. sin(2x) = 2sin(x)sin(x) → False — a cos became a sin; it should read sin(2x) = 2sin(x)cos(x) 4. ln(a*b) = ln(a) + ln(b) → True

entropy in

16 bytes

stream used

41 bytes

rejections

duration

1,017 µs

problems

topic

mixed

true statements

Seed receipt

Class A · Cryptographic degraded

Drawn from the kernel entropy pool on the server that rendered this page. (The source you picked was unreachable, so we fell back to the kernel.)

source: Operating System CSPRNG
observed: 2026-09-13T18:45:44+00:00
latency: 1507ms
mixed with: nothing — this source stands alone

This source publishes no per-draw proof URL.

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The token is the seed, so this link recomputes the result rather than looking it up. No database, and it works for as long as v1 does.

Controls · from schema()

Topic

How many

1 30

Say what is wrong

Prints the correct form beside a false statement.

Entropy source

Picking a source changes the story on the receipt, never the quality: anything below class A is mixed with the OS CSPRNG before it reaches you. This result actually came from Operating System CSPRNG.

seed token D086SM52K7GJEVE8T9KM1JZ7EC

Re-render keeps this token. Generate replaces it. That is the whole idea.

Printable worksheet 20 problems · answers on page 2

The seed is printed in the footer, so the same sheet comes back from the same link — and a different seed is a different sheet.

This page and /api/v1/g/equations.identity run the same code. There is no private endpoint.

True or False?

Result

Measurements

Seed receipt

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