Question

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

Options

• \[x=a\sin\theta\]

• \[x=a\tan\theta\]

• \[x=a\cos\theta\]

• \[x=a\sec\theta\]

Answer 1

For \[a^2-x^2\] or \[\sqrt{a^2-x^2}\], use \[x=a\sin\theta\]. This converts the expression using the identity involving \[1-\sin^2\theta\].