Question

Which standard substitution is used for \[\sqrt{\mathrm{a}^2-x^2}\], \[\frac{1}{\sqrt{\mathrm{a}^2-x^2}}\], or \[\mathrm{a}^2-x^2\]?

Options

• \[x=a\tan\theta\]

• \[x=a\sin^2\theta\]

• \[x=a\sin\theta\] or \[x=a\cos\theta\]

• \[x=a\sec\theta\]

Answer 1

For expressions involving \[\mathrm{a}^2-x^2\], use \[x=a\sin\theta\] or \[x=a\cos\theta\]. These substitutions simplify the radical by a trigonometric identity.