[Merged by Bors] - 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

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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

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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.

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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]

Can you update the profiler comparison comment so that reviewers can know that the second proof isn't that bad?

[yuanyi-350]

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

Results (seconds):

• Complex.cos_three_mul: 0.070367 -> 0.015276 (-78.3%)
• Complex.sin_three_mul: 0.043212 -> 0.030453 (-29.5%)

Overall:

• Both changed declarations got faster.
• Complex.cos_three_mul improved substantially.
• Complex.sin_three_mul also improved, but by a smaller amount.

[yuanyi-350]

!bench

[leanprover-radar]

Benchmark results for 292cd67 against c3e588b are in. No significant results found. @yuanyi-350

• ✅ build//instructions: -5.4G (-0.00%)

Small changes (1✅)

• ✅ build/module/Mathlib.Tactic.MinImports//instructions: -134.0M (-2.60%)

[themathqueen]

maintainer merge

(editing in maintainer merge into a comment from 2 hours ago doesn't work apparently)

[github-actions]

🚀 Pull request has been placed on the maintainer queue by themathqueen.

[bryangingechen]

Thanks!
bors r+

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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