Question

Prove? `cotx/(cscx-1)=(cscx+1)/cotx`

Answer 1

Remember that `1+cot^2x=csc^2x`.

Explanation:

`cotx/(cscx-1)=(cscx+1)/cotx`

Remember that `1+cot^2x=csc^2x`. This becomes useful if we multiply the terms with `cscx` to get them squared:

`cotx/(cscx-1)((cscx+1)/(cscx+1))=(cscx+1)/cotx`

`(cotxcscx+cotx)/(csc^2x-1)=(cscx+1)/cotx`

We can now use `csc^2x-1=cot^2x`

`(cotxcscx+cotx)/(cot^2x)=(cscx+1)/cotx`

`(cscx+1)/(cotx)=(cscx+1)/cotx`