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A secant and a tangent in one sum below the bar are integrated in the half angle - #1855
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Rafael-SOWNet merged 3 commits intoOct 12, 2026
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… out of the sum Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…ent-over-their-shared-factors
…ndard2.0 Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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Part of #718.
1/(a + c sec(x) + b tan(x))and1/(a + b cot(x) + c csc(x)), Rubi's 4.7.7, were declined. Combined over the cosine, the half-angle tangenttgives a denominator with1 + t^2and1 - t^2in every term, and it was read as a quartic with a symbol in every coefficient. The half angle now takes the factors withtin them that every term of a sum shares (inner sums first) out of that sum. The numerator then cancels them, and what is left is a quadratic beside1 + t^2. A baretshared by every term is left alone, because the partial fractions find that root on their own.Measured on master b3805f8:
1/(a + c*sec(x) + b*tan(x))1/(a + b*cot(x) + c*csc(x))1/(a + c*sec(2*x + 1) + b*tan(2*x + 1))Corpus, every family against master b3805f8: 2 moves, 4.7.7:569 and 4.7.7:584, both from unsolved to solved. 0 wrong. The allocation gate passes, and the suite passes 15,248.
The new
ASecantAndATangentInOneSumIntegralTestchecks four rows numerically at pinned constants, with a bound of 4,000 characters.🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura