Maximum and Minimum in Trigonometry

juantheron
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Homework Statement



Find Maximum and Minimum value of

Homework Equations



\mathbf{f(x) = sin^{2n+1}\; x - cos^{2n+1}\; x} and \mathbf{n\in\mathbb{N}}


The Attempt at a Solution



put \mathbf{n=1, f(x) = sin^3\; x -cos^3\; x}\\\\

get \mathbf{-1\leq f(x)\leq 1}
 
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welcome to pf!

hi juantheron! welcome to pf! :wink:

are you allowed to use calculus?​
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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