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

## Answer this Question

## Related Questions

- Integration - Intergrate ¡ì sec^3(x) dx could anybody please check this answer. ...
- Trigonometry desperate help, clueless girl here - 2. solve cos 2x-3sin x cos 2x...
- Trigonometry - 1.Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two ...
- trigonometry hlp me - 6.Prove that tan y cos^2 y + sin^2y/sin y = cos y + sin y...
- trig help much appreciated! :)) - 1. Find the complete exact solution of sin x...
- Math - Prove Trig. Identities 1. sec è (sec è - cos è)= tan^2 è 2. tan^2 è (1 + ...
- Math- gr.12 Trig. - Hi, could someone explain to me how to use a counterexample...
- trig - how do you start this equation i've been tryng it for 20min. sec^6x(...
- trig 26 - simplify to a constant or trig func. 1. sec ²u-tan ²u/cos ²v+sin ²v ...
- trignonmetry - 6. Prove that tan λ cos^2 λ + sin^2λ/sin λ = ...