Request for Reduction Formula derivation (1 Viewer)

[ajtho777]

Hi all, this is the question I'm having a little trouble with:

 

[askit]

Let u = sin^(2n-1)x, dv/dx = sinx, then when u do integration by parts u should get something like sin^(2n-2)x multiplied by cos^2x = 1- sin^2x

 

[aqwerty13402]

this makes me love advanced math

 

[Canteen]

Obviously the competent maths teacher would teach you the beta and gamma function methods, as that gives much quicker solutions.

Your comment and a few recent articles by Derek Buchanan at 4unitmaths.com have both mentioned the beta and gamma functions as alternative, more efficient, approaches to certain questions. Furthermore, in his most recent article 'Alternative solutions to 2023 HSC Extension 1 Q14ci' Derek states that the markers confirmed at the 2024 HSC Feedback Day that the cross product would be an acceptable approach given the question said 'or otherwise'.

This leads me to only conclude that any question including 'or otherwise' may be solved using any mathematical concept (irregardless of whether the syllabus includes it or not) so long as it's correct. Indeed, this may even extend to all questions that don't specify the use of results proved in previous parts (e.g. 'hence' questions) or given in the stem. Am I missing something here?