[Rafael-SOWNet]

Part of #2142: 1 + tan(x)^2 = sec(x)^2, the second pair in its table.

The defect: 1 + tan(x)^2 = sec(x)^2 and 1 + cot(x)^2 = csc(x)^2 are rules in TrigonometricRules for two siblings, so the sort decides whether the 1 and the square meet.

• Secant sorts before tangent, so 1 + tan(x)^2 - sec(x)^2 became 1 - sec(x)^2 + tan(x)^2 and stayed.
• Cotangent sorts before cosecant, so its twin was 0 provided not sin(x) = 0.

The change: both identities are added to PythagoreanIdentity as gathered rules. That set already finds sin^2 + cos^2 wherever the two terms sit in a sum, and #2175 did the same with a coefficient.

• They are SoundUnderAssumptions, as the sibling rules are, since each side is defined only where cos (sin) is not 0.
• Each has a pattern on both sides, is reversible, has growth Collects, and carries its identity.

The census moves by two in WritingARule.md, in the remark in Saturation.cs, and in the tests that pin them. ReversibleRuleTest's hole-dropping check now names the two Pythagorean rules instead of every rule of the set, because these two keep their argument.

Simplify	2.6.0	this PR
1 + tan(x)^2 - sec(x)^2	unchanged	0 provided not cos(x) = 0
a + 1 + tan(y)^2 - sec(y)^2	unchanged	a provided not cos(y) = 0

Still open on #2142:

• The tangent addition formula, half-angle, Weierstrass, sum-to-product and product-to-sum identities.
• The cosine power reduction cos(x)^2 - (1 + cos(2x))/2, whose sine twin is answered. Its candidates reach -1/2 + cos(x)^2/2 + sin(x)^2/2, and the two squares there are quotients rather than products, so neither Pythagorean rule matches them.

Checked:

• TangentSecantIdentityTest: 5 rows.
• The intbench chain against master c90db9f13: identical verdicts in all nine families, 0 moves.
• Performance gate: passed on all 19 gated benchmarks.
• Unit suite: 17,164 passed, 0 failed.
• RuleCheck passes; Confluence and CanonCheck match their baselines; SimpSweep 10,463/10,463.
• BREAKING-CHANGES entry added, measured on the 2.6.0 package.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.46%. Comparing base (c90db9f) to head (9150b4d).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2176      +/-   ##
==========================================
+ Coverage   86.44%   86.46%   +0.01%     
==========================================
  Files         295      295              
  Lines       64930    64969      +39     
  Branches    19092    19092              
==========================================
+ Hits        56130    56176      +46     
+ Misses       4771     4765       -6     
+ Partials     4029     4028       -1     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.03% <100.00%> (+0.01%)	⬆️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
...Math/Core/Transformations/Matching/MatchedRules.cs	99.57% <100.00%> (+<0.01%)	⬆️
...ces/AngouriMath/Core/Transformations/Saturation.cs	93.33% <ø> (ø)

... and 5 files with indirect coverage changes

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