Write the following as a function of x with no trig function

Write the following as a function of x with no trig functions: sin (sec^-1 1/Squareroot 1 - x^2 + csc^-1 Squareroot 1 + x^2)

Let arcsec be A and arccosec be B

That is secA=1/(1-x^2)^1/2 and csc = (1+x^2)1/2

That is CosA =(1-x^2)1/2 SinA =x

Sin B = 1/(1+x^2)1/2 and Cos B =x/(1+x^2)1/2

Now the given expression is

Sin (A+B) = SinA Cos B +CosASinB

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

=[x + (1-x^2)1/2]/(1+x^2)1/2