Verify if arcsinx + arccosx = pi/2 if -1

We'll associate a function f(x) to the expression (arcsin
x + arccos x).

If we want to prove that the function is a
constant function, we'll have to do the first derivative test. If the first derivative
is cancelling, that means that f(x) is a constant function, knowing the fact that a
derivative of a constant function is 0.

f'(x) = (arcsin x +
arccos x)'

f'(x) = 1/sqrt(1-x^2) -
1/sqrt(1-x^2)

We'll eliminate like
terms:

f'(x)=0, so
f(x)=constant

To verify if the constant is pi/2, we'll put
x = 1:

f(1)=arcsin 1 + arccos 1 = pi/2 +
0=pi/2