Question

Which substitution is appropriate for \[\sqrt{\frac{\mathrm{a}-x}{\mathrm{a}+x}}\] or \[\sqrt{\frac{\mathrm{a}+x}{\mathrm{a}-x}}\]?

Options

• \[x=a\sec\theta\]

• \[x=a\tan^2\theta\]

• \[x=a\cos 2\theta\]

• \[x=a\sin\theta\]

Answer 1

For ratios involving \[\mathrm{a}-x\] and \[\mathrm{a}+x\], use \[x=a\cos 2\theta\]. The double-angle expression simplifies both numerator and denominator.