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

1 Answer
Dec 10, 2017

#sqrt((1+sinx)/(1-sinx))=secx+tanx#

Explanation:

#sqrt((1+sinx)/(1-sinx))#

= #sqrt((1+sinx)/(1-sinx)xx(1+sinx)/(1+sinx))#

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

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

= #sqrt((1+sinx)^2/(cos^2x)#

= #(1+sinx)/cosx#

= #1/cosx+sinx/cosx#

= #secx+tanx#