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. sin(a + b) = sin(a)cos(b) + cos(a)sin(b) → True 2. cos(3x) = 4cos(x)^3 - 3cos(x) → True 3. sin(x) = sin(pi/2 - x) → False — a cos became a sin; it should read sin(x) = cos(pi/2 - x) 4. ln(a*b) = ln(a) + exp(b) → False — a ln became a exp; it should read ln(a*b) = ln(a) + ln(b)

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 RANDOM.ORG.

seed token 2C21ECDW8PGVVVAY0T12TPFZ3M

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.

entropy in

16 bytes

stream used

35 bytes

rejections

duration

748 µs

problems

topic

mixed

true statements

Seed receipt

Class A · Cryptographic

Atmospheric radio noise, sampled in Dublin moments ago.

source: RANDOM.ORG
observed: 2026-10-28T23:07:37+00:00
latency: 229ms
mixed with: csprng — always

https://www.random.org/randomness/ ↗

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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.

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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