Question #1bb35

2 Answers
Feb 8, 2017

See below

Explanation:

Cross multiply:

color(green)(cosx)/(color(red)(1+sinx)) = (color(red)(1-sinx))/color(green)(cosx)

implies color(green)(cos^2 x) = color(red)((1 + sin x)(1 - sin x))

implies color(green)(cos^2 x) = color(red)(1 - sin^2 x)

And that is the Pythagorean Identity :)

Feb 9, 2017

LHS=cosx/(1+sinx)

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

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

=(cosx(1-sinx))/cos^2x

=(1-sinx)/cosx=RHS

proved