Question

How do you solve `( tanx+secx)^2 = (1+sinx)/(1-sinx)`?

Answer 1

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

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

= `[-(1 + sin x)]/[-(1 - sin x)]` =`(1 + sin x)/(1 - sin x)`