[Rafael-SOWNet]

Part of #2142: the cosine power reduction.

The defect: sin(x)^2 - (1 - cos(2x))/2 simplified to 0 and cos(x)^2 - (1 + cos(2x))/2 did not. Its candidates reach -1/2 + cos(x)^2 / 2 + sin(x)^2 / 2, which is 0, and stopped there. A rational coefficient is written as a divisor, so k sin(x)^2 + k cos(x)^2 = k (#2175) does not see cos(x)^2 / 2, and the two squares are not siblings for the switch's rules either.

The change: a third gathered rule in PythagoreanIdentity, squared-sine-and-cosine-over-one-divisor-sum-to-its-reciprocal. It gathers sin(x)^2 / d and cos(x)^2 / d with the same argument and the same divisor, and writes 1 / d.

• It is Sound, since both sides are defined exactly where d is not 0.
• It has a pattern on both sides and its growth is Collects.
• It has no backwards reading, since it forgets the angle.
• Two different divisors are left alone.

The census moves by one in WritingARule.md, in the remark in Saturation.cs, and in the tests that pin them.

Simplify	2.6.0	this PR
cos(x)^2 - (1 + cos(2*x))/2	unchanged	0

Checked:

• PowerReductionTest: 5 rows.
• The intbench chain against master 856b3cb6b: identical verdicts in all nine families, 0 moves.
• Performance gate: passed on all 19 gated benchmarks.
• Unit suite: 17,169 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.

Still open on #2142: the tangent addition formula, half-angle, Weierstrass, sum-to-product and product-to-sum identities.

🤖 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 86.45%. Comparing base (856b3cb) to head (020354c).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2177      +/-   ##
==========================================
- Coverage   86.45%   86.45%   -0.01%     
==========================================
  Files         295      295              
  Lines       64969    64995      +26     
  Branches    19092    19092              
==========================================
+ Hits        56171    56193      +22     
- Misses       4770     4775       +5     
+ Partials     4028     4027       -1     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.02% <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	99.58% <100.00%> (+<0.01%)	⬆️
...ces/AngouriMath/Core/Transformations/Saturation.cs	93.33% <ø> (ø)

... and 8 files with indirect coverage changes

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