# #2tan^-1(x)+sin^-1((2x)/(1+x^2))# is independent of #x#, then?

##
a) #x in [1, oo)#

b) #x in (-oo, -1]#

c) #x in [-1,1]#

d) None of these

a)

b)

c)

d) None of these

##### 1 Answer

We start by noticing that the function

Recall that

So we have two inequalities we must solve, which are

#(2x)/(1 + x^2) ≥ -1#

AND

#(2x)/(1 + x^2) ≤ 1#

Let's solve!

#2x ≥ -x^2 - 1#

#x^2 + 2x + 1 ≥ 0#

This is true on all real numbers as

As for the second, we have:

#2x ≤ x^2 + 1#

#0 ≤ x^2 - 2x + 1#

#0 ≤ (x -1)^2#

This also has a solution of all real numbers since it's a parabola which also opens upwards and has it's minimum on the x-axis.

Therefore the answer is

Hopefully this helps!