Trigonometric Identity Verifier & Simplifier mechanism

Model scope

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.

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

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.

Other records

Sources and evidence

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

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