Hello,

Is your question sin^-1((1+x^2)/2x)) + sqrt((cos(sin x))?

Assuming it is then-

To define the value of x for it-

Then we know that value of sqrt((cos(sin x)) will always come as positive.

But (1+x^2)/2x) value should lie between 1 and -1 because of sin-ie

-1 <= (1+x^2)/2x) <= 1

Solving -1 < (1+x^2)/2x)

Hence x^2+1 >= -2x

= (x+1)^2 >= 0 ------(1)

Hence the value of this quantity will also be a positive R value always.

Now solving (1+x^2)/2x) <= 1 similarly we get

(x-1)^2 <= 0 ------(2)

Conditions (1),(2) will be true only at x= 1,-1

Hence in this domain x belongs to only 1 and -1;

x belongs to { 1,-1}

Hope this helps.