Open up multiple angles, and integrate the squares of sine and cosine

[Rafael-SOWNet]

Two things the library could not do, both reached by wiring up machinery that was
already here.

Multiple angles never opened

sin(2x) and cos(2x) stayed as written, so identities in them did not close:

cos(2x) - (1 - 2sin(x)^2)      →  unchanged     now  0
sin(2x) - 2sin(x)cos(x)        →  unchanged     now  0
sin(4x) - 2sin(2x)cos(2x)      →  unchanged     now  0
cos(2x) + sin(x)^2             →  unchanged     now  cos(x)^2

The expansions were not missing. TrigonometricAngleExpansion.ExpandSineArgumentMultiplied
and its cosine twin have been in the tree all along, and were only ever reached for
numeric angles that are multiples of pi. This wires them to a symbolic sin(n x) for
whole n up to 8, past which the expansion is longer than anything it buys.

The expanded form is offered to the simplifier as a candidate, the way the
polynomial factorer's is, so the complexity metric decides. sin(2x) on its own
therefore still prints as sin(2x) — opening it there would only make it longer.

The squares of sine and cosine could not be integrated

∫ sin(x)^2 dx fell through to integration by parts and cycled there until it ran out
of stack. Power reduction, sin(u)^2 = (1 - cos(2u))/2, gives the integral outright, so
it goes in the integral table:

∫ sin(x)^2 dx        →  x/2 - sin(2x)/4
∫ cos(3x)^2 dx       →  x/2 + sin(6x)/12
∫ sin(2x + 1)^2 dx   →  x/2 - sin(2(2x+1))/8

Each is checked by differentiating back at several points, not by comparing strings.

What this does not fix

Worth being explicit, because #557 is the issue this looked like it would close and it
does not:

• Simplify() does not handle complex trigonometrical statements well #557, (sin(2t)csc(t))^2/4 - cos(2t) - sin(t)^2, gets further than before but
  still does not reach 0.
• cos(2x) - (2cos(x)^2 - 1) stops at 1 - cos(x)^2 - sin(x)^2.

Both need a pair of trigonometric terms to be recognised across a subtraction.
sin^2 + cos^2 = 1 is matched as a pair of adjacent terms, and in these two the pair
sits either side of a -. That is the same pairwise-versus-flattened gap as #531, in
trigonometry rather than in a polynomial sum, and opening the angle cannot reach it.
There are tests pinning exactly where each of them stops, so the remaining distance is
recorded rather than implied.

Testing

UnitTests 3676 passed / 0 failed, FSharpWrapperUnitTests 127 passed / 0 failed, and
both netstandard2.0 and net7.0 build.

18 new tests: the identities that close, the two that do not, the compact forms that
must be left alone, value preservation under expansion at several points, and the four
integrals.

Independent of #663 through #670.

🤖 Generated with Claude Code

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Codecov Report

❌ Patch coverage is 94.59459% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 79.49%. Comparing base (90c00a8) to head (c8bf8cc).
⚠️ Report is 41 commits behind head on master.

Files with missing lines	Patch %	Lines
...ouriMath/Functions/Simplification/Simplificator.cs	83.33%	0 Missing and 2 partials ⚠️
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Additional details and impacted files

@@            Coverage Diff             @@
##           master     #671      +/-   ##
==========================================
- Coverage   80.99%   79.49%   -1.50%     
==========================================
  Files         155      155              
  Lines       13687    12331    -1356     
  Branches     1957     1990      +33     
==========================================
- Hits        11086     9803    -1283     
+ Misses       1990     1940      -50     
+ Partials      611      588      -23     

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