SOLUTION: Trigonometry Identities Prove the identity is true 1/cosx

SOLUTION: Trigonometry Identities Prove the identity is true 1/cosx - cosx = sinx tanx

Question 95110: Trigonometry Identities
Prove the identity is true

1/cosx - cosx = sinx tanx
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Here's one way. You will need to use the two identities:
.

and

.
Given:
.

.
substitute for tan(x) to get:
.

.
This substitution changes the right side and the equation becomes:
.

.
Get rid of the denominator by multiplying all the terms on both sides to get:
.

.
Cancel the in the denominator with the corresponding in the numerator:
.

.
and this reduces the equation to:
.

.
Add to both sides to get rid of the on the left side. This
changes the equation to:
.

.
This is in the form of a trigonometric identity that you are probably familiar with already.
Since you have now worked the original given equation into a form known to be true, you
have successfully proved that the original given equation is true.
.
Hope that this helps you to understand the problem.
.

RELATED QUESTIONS
(Sinx+tanx)(sinx�1+cosx)=sinx�tanx prove the identity (answered by josgarithmetic,MathTherapy)

Prove the identity. sinx tanx ---- = -------- sinx+cosx (answered by edjones)

Prove the identity: sinx/(1-cosx) -... (answered by Edwin McCravy)

Cosx/1-sinx - sinx/cosx = 1/cosx Prove the... (answered by Alan3354)

Prove the identity: Cosx/1-sinx - sinx/cosx = 1/cosx (answered by Alan3354)

how to prove trigonometry identity proof: 1+sinx-cosx/1+sinx+cosx =... (answered by jsmallt9,Edwin McCravy)

Prove the identity: (Cosx /1-sinx) - (cosx/1+sinx)... (answered by lwsshak3)

Prove the identity ; (Cosx / 1 -sinx) - ( cosx / 1 +sinx) = 2tanx (answered by Jc0110)

cosx/1-sinx - 1/cosx =tanx prove the following... (answered by HyperBrain)