Proving sec θ (sec θ - cos θ) = tan² θ

[priscilla98]

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 I am 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

 

[Mark44]

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 I am 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.

 

[priscilla98]

Thanks a lot :)