arcsin(x) means "The angle whose sine is x between  and  
arccos(x) means "The angle whose cosine is x" between  and 
"CoSine" means "Complement's Sine 
We must consider two cases.  
Case 1: when x is positive
Then the arcsin(x) and arcos(x) are both in QI
So x will be  
90°-the angle whose sine is x.
But since we are using radians instead of degrees, it is:
 - the angle whose sine is x. 
So 
and therefore

becomes


Multiply through by LCD of 2 to clear the fraction:




Therefore the Case 1 solution is x=1 since 

Case 2: when x is negative
 
Then the arcsin(x) is a negative angle in QIV 
And so 2arcsin(x) is an even more negative angle than arcsin(x)

arccos(x) is a positive angle in QII less than 

So 2arcsin(x)+cos(x) is the sum of a positive angle less than
pi, and a negative angle.  The sum of a positive angle less 
than  added to a negative angle can never equal to , 
so there is no solution to case 2.

Thus the only solution is x=1.

Edwin