Write an algebraic expression in x for sec(arcsin(x/sqrt(x^(2) +4)))

Answer 1

sin A = x/sqrt(x^2+4)

draw that right triangle
side adjacent to A is
sqrt (x^2+4-x^2) = sqrt 4 = 2
so
cos A = 2/sqrt(x^2+4)
sec A = 1/cos A = sqrt(x^2+4)/2