Posted by **Mel** on Tuesday, May 31, 2011 at 9:20pm.

How do I prove the following Identity?

sec x(sec x-cos 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.

- Trig -
**Anonymous**, Tuesday, May 31, 2011 at 10:35pm
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)=

1-cos^2(x)/cos^2(x)

Remark:

sin^2(x)+cos^2(x)=1

sin^2(x)=1-cos^2(x)

1-cos^2(x)/cos^2(x) = sin^2(x)/cos^2(x) = tan^2(x)

- Trig -
**Reiny**, Wednesday, June 1, 2011 at 7:12am
LS = sec x(sec x-cos x)

= (1/cosx)(1/cosx - cosx)

= 1/cos^2x - 1

= sec^2 - 1

= tan^2x (by definition)

= RS

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