Question

For \[\sqrt{\frac{x-\alpha}{\beta-x}}\] or \[\sqrt{(x-\alpha)(\beta-x)}\], where \[\beta>\alpha\], which substitution is used?

Options

• \[x=a\sin^2\theta\]

• \[x=a\cos 2\theta\]

• \[x=\alpha\sin^2\theta+\beta\cos^2\theta\]

• \[x=\alpha\cos^2\theta+\beta\sin^2\theta\]

Answer 1

When \[\beta>\alpha\], use \[x=\alpha\cos^2\theta+\beta\sin^2\theta\]. This substitution is designed for the factors \[x-\alpha\] and \[\beta-x\].