Question

Which substitution is appropriate for \[\sqrt{\frac{x}{a-x}}\], \[\sqrt{\frac{a-x}{x}}\], \[\sqrt{x(a-x)}\], or \[\frac{1}{\sqrt{x(a-x)}}\]?

Options

• \[x=a\sin^2\theta\]

• \[x=a\sec^2\theta\]

• \[x=a\cos\theta\]

• \[x=a\tan^2\theta\]

Answer 1

The forms containing \[x(a-x)\] use \[x=a\sin^2\theta\]. Then \[a-x\] is converted into an expression involving \[\cos^2\theta\].