Question

How do you rationalize the numerator for `sqrt(sinx/cotx)`?

Answer 1

Simplify within the square root first, using the identity `cotx = cosx/sinx`.

`=>sqrt(sinx/(cosx/sinx))`

`=>sqrt(sin^2x/cosx`

`=> sqrt(sin^2x)/sqrt(cosx) xx sqrt(cosx)/sqrt(cosx)`

`=>sqrt(sin^2xcosx)/cosx`

Hopefully this helps!