Question

Prove that `secx-tanx=sqrt((1-sinx)/(1+sinx)`?

Answer 1

Please see below.

Explanation:

`secx-tanx`

= `1/cosx-sinx/cosx`

= `(1-sinx)/cosx`

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

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

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

= `sqrt((1-sinx)^2/((1+sinx)(1-sinx))`

= `sqrt((1-sinx)/(1+sinx)`