Question 242931
{{{a=1/sqrt(1-b^2)}}} Start with the given equation.



{{{a*sqrt(1-b^2)=1}}} Multiply both sides by {{{sqrt(1-b^2)}}}.



{{{sqrt(1-b^2)=1/a}}} Divide both sides by 'a'.



{{{1-b^2=(1/a)^2}}} Square both sides.



{{{1-b^2=1/a^2}}} Square {{{1/a}}} to get {{{1/a^2}}}



{{{-b^2=1/a^2-1}}} Subtract 1 from both sides.



{{{-b^2=1/a^2-(a^2)/(a^2)}}} Multiply 1 by {{{(a^2)/(a^2)}}}



{{{-b^2=(1-a^2)/a^2}}} Combine the fractions.



{{{b^2=-(1-a^2)/a^2}}} Divide both sides by -1.



{{{b^2=(a^2-1)/a^2}}} Distribute



{{{b=""+-sqrt((a^2-1)/a^2)}}} Take the square root of both sides.



{{{b=sqrt((a^2-1)/a^2)}}} or {{{b=-sqrt((a^2-1)/a^2)}}} Break up the plus/minus



{{{b=sqrt(a^2-1)/sqrt(a^2)}}} or {{{b=-sqrt(a^2-1)/sqrt(a^2)}}} Break up the square root.



{{{b=sqrt(a^2-1)/a}}} or {{{b=-sqrt(a^2-1)/a}}} Simplify the square roots in the denominator.



So the solutions are: {{{b=sqrt(a^2-1)/a}}} or {{{b=-sqrt(a^2-1)/a}}}