Explanation on how these solutions can be easily seen

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Explanation on how these solutions can be "easily" seen

Homework Statement



Show that x1(t)=cos(t) and x2(t)=sin(t) are both solutions to the following Equation.

Homework Equations



(d2x/dt2) + x = 0


The Attempt at a Solution



Ok, So I just cannot understand how this can easily be seen! I cannot see it at all!
I know I haven't got any work to show you and that is wrong but I honestly do not know where to start with this.

It is in the middle of some lecture notes and all they say is "this can easily be seen"

Please Help this dummy!:'(
 
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Find the second derivatives of sin(t) and cos(t). Once you do that it should be 'easily seen'.
 


Gosh now I feel super dumb :P Thanks a million!
 

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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