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