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Proving Trig Identities

  • #1

Homework Statement


Prove Trig. Identities

1. sec θ (sec θ - cos θ)= tan^2 θ

Homework Equations



sec θ = 1/cos θ
tan θ = sin θ/ cos θ
cot θ = cos θ / sin θ

The Attempt at a Solution



1. sec θ * sec θ - sec θ * cos θ

1/ cos θ * 1/ cos θ - 1/ cos θ * cos θ

----> cos θ is crosses out by the right but im confused on 1/cos θ. I know 1/cos θ = sec θ. Wait does this problem refer to the pythagorean identity which is 1 + tan^2 θ = sec^2 θ
 

Answers and Replies

  • #2
33,505
5,191

Homework Statement


Prove Trig. Identities

1. sec θ (sec θ - cos θ)= tan^2 θ

Homework Equations



sec θ = 1/cos θ
tan θ = sin θ/ cos θ
cot θ = cos θ / sin θ

The Attempt at a Solution



1. sec θ * sec θ - sec θ * cos θ

1/ cos θ * 1/ cos θ - 1/ cos θ * cos θ

----> cos θ is crosses out by the right but im confused on 1/cos θ. I know 1/cos θ = sec θ. Wait does this problem refer to the pythagorean identity which is 1 + tan^2 θ = sec^2 θ
Use = !
Generally you want to start on one side and end up with the expression on the other side.

sec θ * sec θ - sec θ * cos θ = sec2θ - 1 = ?

In answer to your question, yes.
 
  • #3
Thanks a lot :)
 

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