Question

Which trigonometric substitution is suitable for \[x^2-a^2\] and \[\sqrt{x^2-a^2}\]?

Options

• \[x=a\cos\theta\]

• \[x=a\tan\theta\]

• \[x=a\sin\theta\]

• \[x=a\sec\theta\]

Answer 1

For \[x^2-a^2\] and \[\sqrt{x^2-a^2}\], use \[x=a\sec\theta\]. This matches the trigonometric identity involving \[\sec^2\theta-1\].