Tool · runs in your browser, nothing is sent to a server

Verify a trigonometric identity

Two sides, one question: is this an identity — true for everyangle — or is it only true for some? Type both sides and the tool samples angles, reporting the count it actually checked and the first angle where the claim breaks.

How it decides

Parse both sides. Your writing style is normalised first: sin^2(x),sin²θ and (sin x)^2 all become the same tree, and the tool shows you what it understood.
Sample 12 random angles as a quick screen. Any disagreement stops the run and is reported as a counterexample.
If the screen passes, sample 800 angles and report the worst relative difference found (tolerance 1e-9).
Points where either side is undefined — tan(90°), a zero denominator, √ of a negative — are skipped and counted out loud, never silently treated as agreement.

Numbers printed on this page

Same engine, run at build time — so you can compare what the tool says with what the pages claim:

Two claims checked by the same engine that runs the box above.
Claim	Verdict	Points tested
sin²x + cos²x = 1	equal	400
sin²x + cos²x = cos 2x	unequal — at x = -8.5308 rad the sides are 1.0000 and -0.2154	1
cos(x/2) = √((1 + cos x)/2)	conditional-equal on −180° < x < 180° — fails outside it, e.g. at x = 4.1748 rad: -0.4939 vs 0.4939	400

What it does not do

It does not prove. Sampling cannot prove an identity; it can only disprove one. The proof pages carry the line-by-line arguments.
It does not solve equations. “For which x is this true?” is a different question — this tool answers “is it true for every x?”.
It does not send anything anywhere. No account, no server call, no form post; the URL holds your expression so you can share it.