Cauchy-Schwarz Inequality and Its Relation to Trigonometric Identity

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Homework Statement


what is the relation between cauchy_schwarz inequality and this ;
Sin(a+b)=Sin(a)Cos(b)+Cos(a)Sin(b):biggrin:


Homework Equations





The Attempt at a Solution

 
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Think of it as the dot product of two vectors. From that you can show that, although already obvious, \sin{(a+b)}\leq 1.
 

Thread 'Finding the nth roots of a complex number'

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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