How to prove this trig identity? 1/cosx -cosx = sinx tanx

[Stephxox]

question: 1/cosx -cosx = sinx tanx

This is what I have so far:

RS=sinx (sinx/cosx)
=sin2x/cosx
=1-cos2x/cosx
=1-cosx

Where do I go from here? I'm Stuck

 

[peekaboos]

Re: How Do you prove this trig identity?

You're stuck because this is where you went wrong. (in bold)

RS=sinx (sinx/cosx)
=sin2x/cosx This is wrong
=1-cos2x/cosx
=1-cosx

sinx(sinx/cosx) is equaled to sin^2x/cosx unless you forgot the exponent - not sure.

Anyway the answer is:

LS
1/cosx - cosx
Find common denominator
=1-cosx/cosx
Then 1-cosx is sin^2 by using pythagorean identity.
=sin^2x/cosx

RS
sinx(sinx/cosx)
=sin^2/cosx

LS = RS, identity proven.