Question

How do you verify the identity `1/(secxtanx)=cscx-sinx`?

Answer 1

Please see below.

Explanation:

`secxtanx`

= `1/(1/cosx xxsinx/cosx)`

= `1/(sinx/cos^2x)`

= `cos^2x/sinx`

= `(1-sin^2x)/sinx`

= `1/sinx-sin^2x/sinx`

= `cscx-sinx`