Question

If sin x = p, then prove that `cot x = sqrt(1 - p^2)/p`.

Answer 1

To prove, `cot x = sqrt(1 - p^2)/p`

∵ sin² x + cos² x = 1

p² + cos² x = 1

∴ `cos x = sqrt(1 - p^2)`

Now, `cot x = cos x/sin x`

= `sqrt(1 - p^2)/p`

Hence proved.