How do you simplify cosx/(1+sinx) + (1+sinx)/cosx?

1 Answer
George C.
May 23, 2018

(cos x)/(1 + sin x) + (1 + sin x)/(cos x) = 2 sec x

Explanation:

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

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

color(white)((cos x)/(1 + sin x) + (1 + sin x)/(cos x)) = (2 + 2sinx)/((1+sin x)cos x)

color(white)((cos x)/(1 + sin x) + (1 + sin x)/(cos x)) = (2color(red)(cancel(color(black)((1 + sinx)))))/(color(red)(cancel(color(black)((1+sin x))))cos x)

color(white)((cos x)/(1 + sin x) + (1 + sin x)/(cos x)) = 2/cos x

color(white)((cos x)/(1 + sin x) + (1 + sin x)/(cos x)) = 2sec x

Related questions
See all questions in Proving Identities
Impact of this question
8972 views around the world
You can reuse this answer
Creative Commons License