How do you prove the identity sec u - tan u = cos u/(1+sin u)secutanu=cosu1+sinu ?

1 Answer
Feb 22, 2017

See explanation...

Explanation:

Use:

sec u = 1/cos usecu=1cosu

tan u = sin u/cos utanu=sinucosu

cos^2 u + sin^2 u = 1cos2u+sin2u=1

Then:

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

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

color(white)(sec u - tan u) = (1-sin u)/cos u*(1+sin u)/(1+sin u)secutanu=1sinucosu1+sinu1+sinu

color(white)(sec u - tan u) = (1-sin^2 u)/(cos u(1+sin u))secutanu=1sin2ucosu(1+sinu)

color(white)(sec u - tan u) = cos^2 u/(cos u(1+sin u))secutanu=cos2ucosu(1+sinu)

color(white)(sec u - tan u) = cos u/(1+sin u)secutanu=cosu1+sinu