How do you prove #sec x - cos x = sin x tan x#?
1 Answer
Nov 13, 2015
See explanation...
Explanation:
#sec(x) = 1/cos(x)#
#tan(x) = sin(x)/cos(x)#
#sin^2(x) + cos^2(x) = 1#
So:
#sec(x) - cos(x)#
#= 1/(cos(x)) - cos(x)#
#=1/(cos(x)) - cos^2(x)/cos(x)#
#=(1-cos^2(x))/cos(x)#
#=(sin^2(x))/cos(x)#
#=sin(x)sin(x)/cos(x)#
#=sin(x)tan(x)#
