Proving Trigonometric Identities

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Homework Statement



Prove (using the left side):

sinΘ tanΘ = cosΘ sec^2Θ - cosΘ

Homework Equations





The Attempt at a Solution

 
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sin(\theta)tan(\theta)= \frac{sin(\theta)}{cos(\theta)}tan(\theta)cos(\theta)= \tan^2(\theta)cos(\theta)

Now use the fact that tan^2(\theta)= sec^2(\theta)- 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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