Simplify Trigonometric Expression

[pbonnie]

Homework Statement

Simplify the following trigonometric expression:
cscθtanθsecθ

Homework Equations

tanθ = sinθ/cosθ
sin^2θ + cos^2θ = 1
cscθ = 1/sinθ
secθ = 1/cosθ
cotθ = 1/tanθ

The Attempt at a Solution

I just want to double check my solution.
cscθtanθsecθ = 1/sinθ x sinθ/cosθ x 1/cosθ
= ((sin^2θ + cos^2θ) x sinθ x 1)/sinθ x cosθ x cosθ
= sin^2θ x 1
= sin^2θ

Thank you!

 

[Mark44]

Homework Statement

Simplify the following trigonometric expression:
cscθtanθsecθ

Homework Equations

tanθ = sinθ/cosθ
sin^2θ + cos^2θ = 1
cscθ = 1/sinθ
secθ = 1/cosθ
cotθ = 1/tanθ

The Attempt at a Solution

I just want to double check my solution.
cscθtanθsecθ = 1/sinθ x sinθ/cosθ x 1/cosθ

You're OK to here, but not below. Why not simplify by doing some cancelling?

= ((sin^2θ + cos^2θ) x sinθ x 1)/sinθ x cosθ x cosθ
= sin^2θ x 1
= sin^2θ

Thank you!

 

[Mark44]

cscθtanθsecθ = 1/sinθ x sinθ/cosθ x 1/cosθ
= ((sin^2θ + cos^2θ) x sinθ x 1)/sinθ x cosθ x cosθ

What you have above isn't incorrect, but it isn't helpful, either. I don't know how you got the line that follows (sin^2θ x 1) from this.

 

[pbonnie]

Hmm okay would I cancel out the sinθ in 1/sinθ x sinθ/cosθ x 1/cosθ so it simplifies to 1/cos^2θ?

 

[Mark44]

Yes.

 

[pbonnie]

Oh okay. Thanks :)