Question

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

Options

• \[x=a\csc\theta\]

• \[x=a\sec\theta\]

• \[x=a\tan\theta\]

• \[x=a\sin\theta\]

Answer 1

For \[x^2+a^2\] and \[\sqrt{x^2+a^2}\], the suitable substitution is \[x=a\tan\theta\]. It produces a factor involving \[1+\tan^2\theta\].