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cos(pi - x) is not reduced, nor any shift of cosine or tangent by a multiple of pi/2 #2135
Description
Simplify reduces some shifts of sine by a multiple of π/2, and none of cosine or tangent:
| Input | Simplify |
Should be |
|---|---|---|
sin(pi - x) |
sin(x) |
— |
sin(2*pi - x) |
-sin(x) |
— |
sin(pi/2 - x) |
cos(x) |
— |
sin(pi + x) |
unchanged | -sin(x) |
cos(pi - x) |
unchanged | -cos(x) |
cos(pi + x), cos(x - pi) |
unchanged | -cos(x) |
cos(2*pi - x) |
unchanged | cos(x) |
cos(pi/2 - x) |
unchanged | sin(x) |
tan(pi - x) |
unchanged | -tan(x) |
cos(pi - x) + cos(x) therefore stays as it is, although it is 0. That alone stops the cosine formulas in the first chapter of Modenov's Problems in Geometry from checking (#2131).
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