Question

problem set 2, 4-b) Without calculation, explain why (d/dx)arccosine(x) + (d/dx)arcsin(x) = 0

Answer 1

my friend we can talk about, when??

Answer 2

it is very simple. arccos(x)= (Pi/2) - arcsin(x)
use implicit differentiation to solve for (d/dx)arccosine(x) and you will see that - (d/dx)arccosine(x)=(d/dx)arccosine(x)

Answer 3

Thanks. I had to prove arccos(x) + arcsin(x) = Pi/2 first.(somewhat similar to http://www.proofwiki.org/wiki/Sum_of_Arcsine_and_Arccosine)

Answer 4

Another simple way to come up with this is to refer to the fact that (d/dx)arccosine(x)=-1/sr.(1 - x^2), and (d/x)arcsine(x)=1/sr.(1 - x^2). Therefore their addition is 0.