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Do we need to memorise this identity? (2 Viewers)

leehuan

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Yeah if the constant marks the greatest number of a Pythagorean triple it may be faster to use the auxiliary angle method.
 

Paradoxica

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That's interesting. I have not investigated, but I noticed that in both integrals, {3,4,5} and {5,12,13} are Pythagorean Triples.
It's because of the Auxiliary Transformation takes √a2+b2 for the harmonic coefficient, but since it is a Pythagorean Triple, that coefficient is, by definition, c.
 

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Yeah if the constant marks the greatest number of a Pythagorean triple it may be faster to use the auxiliary angle method.
But in any case, it doesn't need to be a Pythagorean Triple.

As long as asinx + bcosx + c satisfies a2+b2=c2, the Auxiliary Transformation and Tangent Half Angle Substitution are guaranteed to be nice.
 

leehuan

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But in any case, it doesn't need to be a Pythagorean Triple.

As long as asinx + bcosx + c satisfies a2+b2=c2, the Auxiliary Transformation and Tangent Half Angle Substitution are guaranteed to be nice.
Yeah basically point is to use one or the other
 

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