refactor(Analysis): golf Mathlib/Analysis/Complex/Trigonometric

[yuanyi-350]

• rewrites cos_three_mul via cosh_three_mul and the cosh_mul_I conversion
• shortens sin_three_mul using sin_add, double-angle identities, and grind

Extracted from #37968

[github-actions]

PR summary c3e588b468

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

No declarations were harmed in the making of this PR! 🐙

You can run this locally as follows

## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[yuanyi-350]

I ran a profiler comparison for the changed declarations in this PR.

Results (seconds):

• Complex.cos_three_mul: 0.061700 -> 0.006364 (-89.7%)
• Complex.sin_three_mul: 0.046297 -> 0.131374 (+183.8%)

Overall:

• Complex.cos_three_mul is much faster.
• Complex.sin_three_mul is slower, mainly from the new grind step.

[themathqueen]

Since the performance is worse, maybe do this instead:

Suggested change

	grind [cos_two_mul, sin_two_mul, cos_sq']
	simp only [cos_two_mul, sin_two_mul, cos_sq', mul_assoc, ← sq]
	ring

same proof as before, but without the haves. Should probably have the same performance.