Trigonometric Identity Verifier & Simplifier

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mathematics — arithmetic through advanced (algebra, matrices, calculus, sequences/series, number theory, combinatorics, graphing, complex numbers, geometry, logic, sets)

Tranche

tranche-8

Evidence ID

t8-034

Ledger rows

1

No ledger note is attached.

Review findings

The core identities tested here are mathematically correct. The verdict is NEEDS_REVIEW because the angle unit convention and numerical verification policy are unspecified, and because the simplifier must preserve original domains rather than reporting only an algebraically equivalent expression.

Formula and scope findings

• The listed Pythagorean, sum/difference, double/half-angle, and product-to-sum identities are standard and correct, but the specification does not define the supported expression grammar or the complete transformation rules.
• Identity verification by finitely many numerical samples can produce false positives and is not a formal proof; the honest label correctly acknowledges this limitation.
• Domain restrictions are required before simplification. For example, (1-cos(2x))/sin(2x)=tan(x) is valid only where sin(2x) is nonzero, so cancellation or rewriting must not silently enlarge the domain.

Unit assumptions

• Angles are assumed to be in radians because symbolic constants such as pi are used. Degree-mode behavior is unspecified and must be stated or implemented explicitly.
• All trigonometric functions are assumed to use dimensionless angle arguments; degree inputs require explicit conversion by angle*pi/180.
• Numerical spot-check tolerances and the sampling strategy are unspecified; samples must avoid poles and undefined expressions unless the expected result is explicitly undefined.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The verifier must explicitly reject undefined samples such as tan(pi/2), preserve absolute-value branch behavior in sqrt(sin(x)^2), and require an angle-unit convention. Otherwise it can return misleading finite values, an invalid global simplification, or a wrong identity verdict.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "expression": "sin(x)^2 + cos(x)^2",
    "sample_points": [
      "x=0",
      "x=pi/6",
      "x=pi/4"
    ]
  },
  "expected_outputs": {
    "simplified_form": "1",
    "identity_verdict": true,
    "spot_checks": [
      {
        "at": {
          "x": 0
        },
        "input_side": 1,
        "answer_side": 1
      },
      {
        "at": {
          "x": 0.5235987756
        },
        "input_side": 1,
        "answer_side": 1
      },
      {
        "at": {
          "x": 0.7853981634
        },
        "input_side": 1,
        "answer_side": 1
      }
    ]
  },
  "reference_data": {
    "identity": "sin(x)^2+cos(x)^2=1",
    "domain": "all real x"
  },
  "working": "At x=0: sin(0)^2+cos(0)^2=0^2+1^2=1. At x=pi/6: (1/2)^2+(sqrt(3)/2)^2=1/4+3/4=1. At x=pi/4: (sqrt(2)/2)^2+(sqrt(2)/2)^2=1/2+1/2=1."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche8/tranche8-results.json
• BOUNDARY_HAZARD_CATALOG.json