If sin x + a cos x = b, then what is the expression for |a sin x - cos x| in terms of a and b?
(A) <span class="math-tex">\(\rm \sqrt{a^2-b^2-1}\)</span>
(B) <span class="math-tex">\(\rm \sqrt{a^2+b^2-1}\)</span>
(C) <span class="math-tex">\(\rm \sqrt{a^2+b^2+1}\)</span>
(D) <span class="math-tex">\(\rm \sqrt{a^2-b^2+1}\)</span>