Question

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

Options

• \[x=a\tan\theta\]

• \[x=a\cos 2\theta\]

• \[x=a\sin\theta\]

• \[x=a\sec\theta\]

Answer 1

The standard substitution for \[x^2+\mathrm{a}^2\] is \[x=a\tan\theta\]. It converts the expression into one involving \[\sec^2\theta\].