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

2 Answers
Bdub
Oct 3, 2016

see below

Explanation:

(1+sinx)/(1-sinx)=(secx+tanx)^2

Right Side =(secx+tanx)^2

=(secx+tanx)(secx+tanx)

=sec^2x+2secxtanx+tan^2x

=1/cos^2x +2*1/cosx *sinx/cosx +sin^2x/cos^2x

=(1+2sinx+sin^2x)/cos^2x

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

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

=(1+sinx)/(1-sinx

= Left Side

Ananda Dasgupta ยท P dilip_k
Feb 20, 2018

A simpler derivation is given below :

Explanation:

{1+sin x}/{1-sin x} = {1+sin x}/{1-sin x} times {1+sin x}/{1+sin x} = {(1+sin x)^2}/{1-sin^2 x} = {(1+sin x)^2}/{cos^2x} = ({1+sin x}/{cos x})^2 = (sec x + tan x)^2

Related questions
See all questions in Proving Identities
Impact of this question
71230 views around the world
You can reuse this answer
Creative Commons License