Trig
posted by Mel on .
How do I prove the following Identity?
sec x(sec xcos x)=tan^2x
If there is a certain website or suggestion to help with these type of equations I would greatly appreciate it. I've been studying these for a while but still get pretty confused.

sec(x)*[sec(x)cos(x)]=
sec(x)*sec(x)sec(x)*cos(x)
Remark:
sec(x)=1/cos(x)
sec(x)*sec(x)sec(x)*cos(x)=
1/cos(x) * 1/cos(x)  1/cos(x) * cos(x)=
1/cos^2(x)1=
1/cos^2(x)  cos^2(x)/cos^2(x)=
1cos^2(x)/cos^2(x)
Remark:
sin^2(x)+cos^2(x)=1
sin^2(x)=1cos^2(x)
1cos^2(x)/cos^2(x) = sin^2(x)/cos^2(x) = tan^2(x) 
LS = sec x(sec xcos x)
= (1/cosx)(1/cosx  cosx)
= 1/cos^2x  1
= sec^2  1
= tan^2x (by definition)
= RS