Question

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

Options

• \[x=a\tan^2\theta\]

• \[x=a\sin\theta\]

• \[x=a\sec\theta\]

• \[x=a\tan\theta\]

Answer 1

For an expression involving \[x^2-a^2\], use \[x=a\sec\theta\]. This produces the identity \[\sec^2\theta-1=\tan^2\theta\].