How do you prove the identity sec u - tan u = cos u/(1+sin u) ?

1 Answer
George C.
Feb 22, 2017

See explanation...

Explanation:

Use:

sec u = 1/cos u

tan u = sin u/cos u

cos^2 u + sin^2 u = 1

Then:

sec u - tan u = 1/cos u - sin u/cos u

color(white)(sec u - tan u) = (1-sin u)/cos u

color(white)(sec u - tan u) = (1-sin u)/cos u*(1+sin u)/(1+sin u)

color(white)(sec u - tan u) = (1-sin^2 u)/(cos u(1+sin u))

color(white)(sec u - tan u) = cos^2 u/(cos u(1+sin u))

color(white)(sec u - tan u) = cos u/(1+sin u)

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